This document outlines Emiliano Sefusatti's presentation on testing the initial conditions of the universe using data from the Planck satellite. The presentation covers predictions from inflation like a flat, homogeneous universe with a nearly scale-invariant power spectrum. It discusses how Planck improved constraints on non-Gaussianity parameters like fNL compared to WMAP. For example, Planck reduced errors on the local fNL parameter by a factor of 2-4 depending on the shape. The implications of Planck's results are explored through the example of constraints on a DBI inflation model.
"When the top is not single: a theory overview from monotop to multitops" to...Rene Kotze
This document discusses potential deviations from the standard model in top quark pair production (ttbar) due to beyond standard model (BSM) physics. It summarizes that ttbar production is well measured but sensitive to BSM effects like resonant contributions from new particles that decay to top quark pairs. Non-resonant effects are also possible and can be parameterized using effective field theory operators. The document provides examples of limits set on specific BSM models like Z' bosons by the CMS experiment through analyses of the ttbar invariant mass spectrum and other observables.
This document summarizes a presentation about reconstructing inflationary models in modified f(R) gravity. It discusses the current status of inflation based on Planck data, reviews how inflation works in f(R) gravity, and describes two approaches - the direct approach of comparing models to data and the inverse approach of smoothly reconstructing models from observational quantities like the scalar spectrum index. A key model discussed is the simple R + R^2 model that can match current measurements of the spectral index and tensor-to-scalar ratio.
The document discusses separating gravitational redshift from cosmic expansion redshift in observed cosmic microwave background radiation. It presents calculations of curvature ratios at different points in the early universe, such as at electroweak symmetry breaking and at the surface of last scattering. Taking the curvature ratio at these two points and using observed CMB redshift of 1091, the analysis estimates gravitational redshift would be around 2-3, with most of the observed redshift coming from cosmic expansion. This has implications for the energy density and relativistic nature of the early universe.
This document outlines a presentation on thermodynamics of anti-de Sitter black holes as regularized fidelity susceptibility. It introduces concepts like entanglement entropy, the holographic principle, and holographic entanglement entropy. It then discusses fidelity susceptibility and holographic complexity. The document derives formulas for these quantities for Reissner-Nordström anti-de Sitter black holes. Specifically, it derives an expression for the difference in entanglement entropy between the pure background and metric deformation. It also computes the holographic complexity and fidelity susceptibility volumes for RN black holes through integrals involving the metric function.
N. Bilic - "Hamiltonian Method in the Braneworld" 3/3SEENET-MTP
This document discusses various models for dark energy and dark matter unification, including quintessence, k-essence, phantom quintessence, Chaplygin gas, and tachyon condensates. It provides field theory descriptions and equations of state for these models. It also discusses issues like the sound speed and structure formation problems that arise for some unified dark energy/dark matter models. Modifications to address these issues, such as generalized Chaplygin gas and variable Chaplygin gas models, are presented.
"When the top is not single: a theory overview from monotop to multitops" to...Rene Kotze
This document discusses potential deviations from the standard model in top quark pair production (ttbar) due to beyond standard model (BSM) physics. It summarizes that ttbar production is well measured but sensitive to BSM effects like resonant contributions from new particles that decay to top quark pairs. Non-resonant effects are also possible and can be parameterized using effective field theory operators. The document provides examples of limits set on specific BSM models like Z' bosons by the CMS experiment through analyses of the ttbar invariant mass spectrum and other observables.
This document summarizes a presentation about reconstructing inflationary models in modified f(R) gravity. It discusses the current status of inflation based on Planck data, reviews how inflation works in f(R) gravity, and describes two approaches - the direct approach of comparing models to data and the inverse approach of smoothly reconstructing models from observational quantities like the scalar spectrum index. A key model discussed is the simple R + R^2 model that can match current measurements of the spectral index and tensor-to-scalar ratio.
The document discusses separating gravitational redshift from cosmic expansion redshift in observed cosmic microwave background radiation. It presents calculations of curvature ratios at different points in the early universe, such as at electroweak symmetry breaking and at the surface of last scattering. Taking the curvature ratio at these two points and using observed CMB redshift of 1091, the analysis estimates gravitational redshift would be around 2-3, with most of the observed redshift coming from cosmic expansion. This has implications for the energy density and relativistic nature of the early universe.
This document outlines a presentation on thermodynamics of anti-de Sitter black holes as regularized fidelity susceptibility. It introduces concepts like entanglement entropy, the holographic principle, and holographic entanglement entropy. It then discusses fidelity susceptibility and holographic complexity. The document derives formulas for these quantities for Reissner-Nordström anti-de Sitter black holes. Specifically, it derives an expression for the difference in entanglement entropy between the pure background and metric deformation. It also computes the holographic complexity and fidelity susceptibility volumes for RN black holes through integrals involving the metric function.
N. Bilic - "Hamiltonian Method in the Braneworld" 3/3SEENET-MTP
This document discusses various models for dark energy and dark matter unification, including quintessence, k-essence, phantom quintessence, Chaplygin gas, and tachyon condensates. It provides field theory descriptions and equations of state for these models. It also discusses issues like the sound speed and structure formation problems that arise for some unified dark energy/dark matter models. Modifications to address these issues, such as generalized Chaplygin gas and variable Chaplygin gas models, are presented.
Prospects for CMB lensing-galaxy clustering cross-correlations and initial co...Marcel Schmittfull
The lensing convergence measurable with future CMB experiments will be highly correlated with the clustering of galaxies that will be observed by imaging surveys such as LSST. I will discuss prospects for using that cross-correlation signal to constrain local primordial non-Gaussianity, the amplitude of matter fluctuations as a function of redshift, halo bias, and possibly the sum of neutrino masses. A key limitation for such analyses and large-scale structure analyses in general is that the mapping from initial conditions to observables is nonlinear for wavenumbers k>0.1h/Mpc. This can destroy cosmological information or move it to non-Gaussian tails of the probability distribution that are difficult to measure. I will describe how we can use recently developed initial condition reconstruction methods to help us recover some of that information in the nonlinear regime.
D. Mladenov - On Integrable Systems in CosmologySEENET-MTP
Lecture by Prof. Dr. Dimitar Mladenov (Theoretical Physics Department, Faculty of Physics, Sofia University, Bulgaria) on December 7, 2011 at the Faculty of Science and Mathematics, Nis, Serbia.
N. Bilić: AdS Braneworld with Back-reactionSEENET-MTP
- A 3-brane moving in an AdS5 background of the Randall-Sundrum model behaves like a tachyon field with an inverse quartic potential.
- When including the back-reaction of the radion field, the tachyon Lagrangian is modified by its interaction with the radion. As a result, the effective equation of state obtained by averaging over large scales describes a warm dark matter.
- The dynamical brane causes two effects of back-reaction: 1) the geometric tachyon affects the bulk geometry, and 2) the back-reaction qualitatively changes the tachyon by forming a composite substance with the radion and a modified equation of state.
MTH101 - Calculus and Analytical Geometry- Lecture 37Bilal Ahmed
Virtual University
Course MTH101 - Calculus and Analytical Geometry
Lecture No 37
Instructor's Name: Dr. Faisal Shah Khan
Course Email: mth101@vu.edu.pk
N. Bilic - "Hamiltonian Method in the Braneworld" 1/3SEENET-MTP
This document provides an overview of the Hamiltonian method in braneworld cosmology. It begins with introductory lectures on preliminaries like Legendre transformations, thermodynamics, fluid mechanics, and basic cosmology. It then covers braneworld universes, strings and branes, and the Randall-Sundrum model. The document concludes with applications of the Hamiltonian method to topics like quintessence, dark energy/matter unification, and tachyon condensates in braneworlds.
- The document discusses a braneworld model where a 3-brane moves in a 5-dimensional anti-de Sitter bulk. The brane behaves effectively as a tachyon field with an inverse quartic potential.
- When the backreaction of the radion field (related to fluctuations of the brane position) is included, the tachyon Lagrangian is modified by its interaction with the radion. This results in an effective equation of state at large scales that describes "warm dark matter".
- The model extends the second Randall-Sundrum braneworld model to include nonlinear effects from the radion field, which distorts the anti-de Sitter geometry.
I. Cotaescu - "Canonical quantization of the covariant fields: the Dirac fiel...SEENET-MTP
The document discusses the canonical quantization of covariant fields on curved spacetimes, specifically the de Sitter spacetime. It introduces covariant fields that transform under representations of the spin group SL(2,C) and have covariant derivatives ensuring gauge invariance. Isometries of the spacetime generate Killing vectors and induce representations of the external symmetry group, which is the universal covering group of isometries and combines isometries with gauge transformations. Generators of these representations provide conserved observables that allow canonical quantization analogous to special relativity. The paper focuses on applying this framework to the Dirac field on de Sitter spacetime.
Dr. Mukesh Kumar (NITheP/Wits) TITLE: "Top quark physics in the Vector Color-...Rene Kotze
This document presents a vector color-octet model to explain anomalies observed in top quark physics measurements at the Tevatron collider. The model introduces new vector color-octet resonances that can contribute to top quark pair production and give rise to asymmetries. Observables related to the top quark like the forward-backward asymmetry, charge asymmetry, and single top production are discussed. Constraints on the masses of the new vector resonances from LHC data are also presented. Simulation tools like MadGraph are used to study predictions of the model.
Fractales bartolo luque - curso de introduccion sistemas complejosFundacion Sicomoro
¿Qué tienen en común los brócolis, las nubes y los cráteres meteoríticos? Todos exhiben fractalidad. Una nueva ciencia como la de los Sistemas Complejos, requería una nueva manera de caracterizar las formas: la geometría fractal. En esta charla aprenderemos qué es un fractal, dónde aparecen, dónde se usan y qué nos desvelan. Veremos que, en el fondo, la invarianza de escala, que va más allá de la geometría, es el concepto crucial.
This document is a dissertation proposal by Rishideep Roy at the University of Chicago in November 2014. The proposal is to generalize results on extreme values and entropic repulsion for two-dimensional discrete Gaussian free fields to a more general class of Gaussian fields with logarithmic correlations. Specifically, the proposal plans to find the convergence in law of the maximum of these log-correlated Gaussian fields under minimal assumptions, as well as obtain finer estimates on entropic repulsion which relates to the behavior of these fields near hard boundaries. The proposal provides background on related works and outlines the key steps to be taken, including proving expectations and tightness of maxima, invariance of maximum distributions under perturbations, approximating the fields, and
- The document discusses going beyond the standard model of cosmology which assumes a flat Lambda Cold Dark Matter (LCDM) universe with a power-law primordial spectrum.
- It suggests that the universe could be more complicated and that extensions to the standard model need to be properly investigated using advanced statistical methods and high quality observational data.
- Examples of possible extensions discussed include allowing the primordial power spectrum to take on different forms beyond a simple power law, or exploring the possibility that dark energy is not a cosmological constant.
The document presents two solutions to the problem of a rope falling through a hole.
(1) Using conservation of energy, the first solution finds the final speed is √gL. However, this assumes an instantaneous fall, which is unrealistic.
(2) The second solution treats the rope as continuously accelerating downward. Applying Newton's second law F=ma to the moving portion of rope, the acceleration is found to be g/3. The final speed is then 2√gL/3.
This second solution is more accurate as it accounts for the rope accumulating mass over time during the fall.
1) The document analyzes polarization features in bistatic scattering from rough surfaces using analytical methods like SPM, PO, and SSA/RLCA.
2) SPM predicts nulls in certain polarization configurations depending on permittivity and scattering angles. PO and SSA/RLCA transitions these predictions depending on roughness.
3) Numerical simulations using MOM agree with SSA/RLCA and show the transition of null regions with increasing roughness.
4) Understanding these polarization effects could help design bistatic remote sensing systems or interpret results from previous studies of soil moisture sensing.
All of the perturbative approaches to multidimensional wave
equation processing. for example. wave equation migration (see,
e.g., Claerbout, 1971; French, 1975: Schneider, 1978; Stolt, 1978;
Sattlegger et al, 1980), or Born approximation inversion (see,
e.g., Cohen and Bleistein, 1979; Raz, 1981: Clayton and Stolt,
1981) require some input velocity information. In the Born approximation
to inversion, a reference or background velocity is
chosena nd a perturbationa boutt his velocity is determined.S imilarly,
a velocity model is a required input to all wave equation
migration techniques.
D. Vulcanov, REM — the Shape of Potentials for f(R) Theories in Cosmology and...SEENET-MTP
This document summarizes a presentation given at the 2013 Balkan Workshop in Vrnjacka Banja, Serbia on using the "reverse engineering method" (REM) to model cosmology. The presentation reviewed REM and how it can be used to determine scalar field potentials from a given scale factor evolution. Computer programs for numerically and graphically processing REM with different cosmologies were discussed. Examples presented included regular and tachyonic potentials, and cosmology with non-minimally coupled scalar fields and f(R) gravity. Specific examples plotted potentials and scale factors for exponential and linear expansion universes. The presentation concluded with references for further reading on REM and its applications in cosmology.
PDE Constrained Optimization and the Lambert W-FunctionMichael Maroun
This document discusses using the Lambert W-function to solve partial differential equations (PDEs) that arise from optimization problems with PDE constraints. It first presents an example optimization problem involving minimizing the difference between a disk's actual and ideal temperature distributions. Solving the resulting PDE system may involve the Lambert W-function. It then briefly introduces the Lambert W-function and shows how it relates solutions of linear and nonlinear differential equations. Finally, it presents another nonlinear PDE whose solution involves the Lambert W-function.
Seismic data processing 14, stacking&migration2Amin khalil
This document summarizes seismic data processing techniques like stacking and migration. It discusses Huygen's principle, how diffraction works using examples, and how stacking can be used to obtain diffraction points by using the proper velocity. It also explains how migration works by applying concepts to multiple diffractor points, and how a dipping reflector can be mapped through migration by a cosine term. The document provides examples and illustrations of key concepts in seismic data processing like diffraction stacking, four point diffractors, and addressing issues like bow-tie phenomena through migration techniques.
This document discusses Buckingham's pi-theorem, which states that any physically meaningful relationship between physical quantities can be expressed in terms of dimensionless combinations of those quantities. The document provides an example applying the theorem to the problem of fluid flow through a pipe. Specifically, it shows that the pressure drop through the pipe can be expressed as a function of Reynolds number, relative roughness, and Fanning's friction factor.
This document summarizes a presentation on using the 4th order Runge-Kutta method to model the trajectory of projectiles. It discusses ordinary differential equations, introduces the RK4 method, and applies it to model the trajectory of unguided missiles accounting for gravity and drag forces, as well as guided self-propelled missiles where thrust is also considered. Input parameters for a simulation of a North Korean missile are provided and the optimal range is determined. Limitations of the model and references are also noted.
VariableR jet reclustering is a technique that reconstructs boosted objects like top quarks and W bosons over a wide kinematic range. It does this by varying the radius of reclustering, unlike fixed radius reclustering. When evaluating performance on events with multiple top quarks, VariableR reclustering identifies top quark candidates with masses closer to the actual top quark mass and has a higher reconstruction efficiency than fixed radius reclustering. This enhances sensitivity for searches of new particles that decay into top quarks, like gluinos.
Y. Sitenko: Vacuum Polarization Effects in the Cosmic String Background and P...SEENET-MTP
- The document summarizes research on vacuum polarization effects caused by cosmic strings and primordial magnetic fields in the universe.
- Cosmic strings formed in the early universe through spontaneous symmetry breaking and have properties like linear energy density and inducing vacuum currents that generate magnetic fields.
- Calculations are presented for the induced vacuum energy-momentum tensor in the background of a cosmic string, which depends on the string's properties and the spacetime metric.
- Primordial magnetic fields on galactic or larger scales could have originated from phenomena like superconducting cosmic strings in the early universe.
Prospects for CMB lensing-galaxy clustering cross-correlations and initial co...Marcel Schmittfull
The lensing convergence measurable with future CMB experiments will be highly correlated with the clustering of galaxies that will be observed by imaging surveys such as LSST. I will discuss prospects for using that cross-correlation signal to constrain local primordial non-Gaussianity, the amplitude of matter fluctuations as a function of redshift, halo bias, and possibly the sum of neutrino masses. A key limitation for such analyses and large-scale structure analyses in general is that the mapping from initial conditions to observables is nonlinear for wavenumbers k>0.1h/Mpc. This can destroy cosmological information or move it to non-Gaussian tails of the probability distribution that are difficult to measure. I will describe how we can use recently developed initial condition reconstruction methods to help us recover some of that information in the nonlinear regime.
D. Mladenov - On Integrable Systems in CosmologySEENET-MTP
Lecture by Prof. Dr. Dimitar Mladenov (Theoretical Physics Department, Faculty of Physics, Sofia University, Bulgaria) on December 7, 2011 at the Faculty of Science and Mathematics, Nis, Serbia.
N. Bilić: AdS Braneworld with Back-reactionSEENET-MTP
- A 3-brane moving in an AdS5 background of the Randall-Sundrum model behaves like a tachyon field with an inverse quartic potential.
- When including the back-reaction of the radion field, the tachyon Lagrangian is modified by its interaction with the radion. As a result, the effective equation of state obtained by averaging over large scales describes a warm dark matter.
- The dynamical brane causes two effects of back-reaction: 1) the geometric tachyon affects the bulk geometry, and 2) the back-reaction qualitatively changes the tachyon by forming a composite substance with the radion and a modified equation of state.
MTH101 - Calculus and Analytical Geometry- Lecture 37Bilal Ahmed
Virtual University
Course MTH101 - Calculus and Analytical Geometry
Lecture No 37
Instructor's Name: Dr. Faisal Shah Khan
Course Email: mth101@vu.edu.pk
N. Bilic - "Hamiltonian Method in the Braneworld" 1/3SEENET-MTP
This document provides an overview of the Hamiltonian method in braneworld cosmology. It begins with introductory lectures on preliminaries like Legendre transformations, thermodynamics, fluid mechanics, and basic cosmology. It then covers braneworld universes, strings and branes, and the Randall-Sundrum model. The document concludes with applications of the Hamiltonian method to topics like quintessence, dark energy/matter unification, and tachyon condensates in braneworlds.
- The document discusses a braneworld model where a 3-brane moves in a 5-dimensional anti-de Sitter bulk. The brane behaves effectively as a tachyon field with an inverse quartic potential.
- When the backreaction of the radion field (related to fluctuations of the brane position) is included, the tachyon Lagrangian is modified by its interaction with the radion. This results in an effective equation of state at large scales that describes "warm dark matter".
- The model extends the second Randall-Sundrum braneworld model to include nonlinear effects from the radion field, which distorts the anti-de Sitter geometry.
I. Cotaescu - "Canonical quantization of the covariant fields: the Dirac fiel...SEENET-MTP
The document discusses the canonical quantization of covariant fields on curved spacetimes, specifically the de Sitter spacetime. It introduces covariant fields that transform under representations of the spin group SL(2,C) and have covariant derivatives ensuring gauge invariance. Isometries of the spacetime generate Killing vectors and induce representations of the external symmetry group, which is the universal covering group of isometries and combines isometries with gauge transformations. Generators of these representations provide conserved observables that allow canonical quantization analogous to special relativity. The paper focuses on applying this framework to the Dirac field on de Sitter spacetime.
Dr. Mukesh Kumar (NITheP/Wits) TITLE: "Top quark physics in the Vector Color-...Rene Kotze
This document presents a vector color-octet model to explain anomalies observed in top quark physics measurements at the Tevatron collider. The model introduces new vector color-octet resonances that can contribute to top quark pair production and give rise to asymmetries. Observables related to the top quark like the forward-backward asymmetry, charge asymmetry, and single top production are discussed. Constraints on the masses of the new vector resonances from LHC data are also presented. Simulation tools like MadGraph are used to study predictions of the model.
Fractales bartolo luque - curso de introduccion sistemas complejosFundacion Sicomoro
¿Qué tienen en común los brócolis, las nubes y los cráteres meteoríticos? Todos exhiben fractalidad. Una nueva ciencia como la de los Sistemas Complejos, requería una nueva manera de caracterizar las formas: la geometría fractal. En esta charla aprenderemos qué es un fractal, dónde aparecen, dónde se usan y qué nos desvelan. Veremos que, en el fondo, la invarianza de escala, que va más allá de la geometría, es el concepto crucial.
This document is a dissertation proposal by Rishideep Roy at the University of Chicago in November 2014. The proposal is to generalize results on extreme values and entropic repulsion for two-dimensional discrete Gaussian free fields to a more general class of Gaussian fields with logarithmic correlations. Specifically, the proposal plans to find the convergence in law of the maximum of these log-correlated Gaussian fields under minimal assumptions, as well as obtain finer estimates on entropic repulsion which relates to the behavior of these fields near hard boundaries. The proposal provides background on related works and outlines the key steps to be taken, including proving expectations and tightness of maxima, invariance of maximum distributions under perturbations, approximating the fields, and
- The document discusses going beyond the standard model of cosmology which assumes a flat Lambda Cold Dark Matter (LCDM) universe with a power-law primordial spectrum.
- It suggests that the universe could be more complicated and that extensions to the standard model need to be properly investigated using advanced statistical methods and high quality observational data.
- Examples of possible extensions discussed include allowing the primordial power spectrum to take on different forms beyond a simple power law, or exploring the possibility that dark energy is not a cosmological constant.
The document presents two solutions to the problem of a rope falling through a hole.
(1) Using conservation of energy, the first solution finds the final speed is √gL. However, this assumes an instantaneous fall, which is unrealistic.
(2) The second solution treats the rope as continuously accelerating downward. Applying Newton's second law F=ma to the moving portion of rope, the acceleration is found to be g/3. The final speed is then 2√gL/3.
This second solution is more accurate as it accounts for the rope accumulating mass over time during the fall.
1) The document analyzes polarization features in bistatic scattering from rough surfaces using analytical methods like SPM, PO, and SSA/RLCA.
2) SPM predicts nulls in certain polarization configurations depending on permittivity and scattering angles. PO and SSA/RLCA transitions these predictions depending on roughness.
3) Numerical simulations using MOM agree with SSA/RLCA and show the transition of null regions with increasing roughness.
4) Understanding these polarization effects could help design bistatic remote sensing systems or interpret results from previous studies of soil moisture sensing.
All of the perturbative approaches to multidimensional wave
equation processing. for example. wave equation migration (see,
e.g., Claerbout, 1971; French, 1975: Schneider, 1978; Stolt, 1978;
Sattlegger et al, 1980), or Born approximation inversion (see,
e.g., Cohen and Bleistein, 1979; Raz, 1981: Clayton and Stolt,
1981) require some input velocity information. In the Born approximation
to inversion, a reference or background velocity is
chosena nd a perturbationa boutt his velocity is determined.S imilarly,
a velocity model is a required input to all wave equation
migration techniques.
D. Vulcanov, REM — the Shape of Potentials for f(R) Theories in Cosmology and...SEENET-MTP
This document summarizes a presentation given at the 2013 Balkan Workshop in Vrnjacka Banja, Serbia on using the "reverse engineering method" (REM) to model cosmology. The presentation reviewed REM and how it can be used to determine scalar field potentials from a given scale factor evolution. Computer programs for numerically and graphically processing REM with different cosmologies were discussed. Examples presented included regular and tachyonic potentials, and cosmology with non-minimally coupled scalar fields and f(R) gravity. Specific examples plotted potentials and scale factors for exponential and linear expansion universes. The presentation concluded with references for further reading on REM and its applications in cosmology.
PDE Constrained Optimization and the Lambert W-FunctionMichael Maroun
This document discusses using the Lambert W-function to solve partial differential equations (PDEs) that arise from optimization problems with PDE constraints. It first presents an example optimization problem involving minimizing the difference between a disk's actual and ideal temperature distributions. Solving the resulting PDE system may involve the Lambert W-function. It then briefly introduces the Lambert W-function and shows how it relates solutions of linear and nonlinear differential equations. Finally, it presents another nonlinear PDE whose solution involves the Lambert W-function.
Seismic data processing 14, stacking&migration2Amin khalil
This document summarizes seismic data processing techniques like stacking and migration. It discusses Huygen's principle, how diffraction works using examples, and how stacking can be used to obtain diffraction points by using the proper velocity. It also explains how migration works by applying concepts to multiple diffractor points, and how a dipping reflector can be mapped through migration by a cosine term. The document provides examples and illustrations of key concepts in seismic data processing like diffraction stacking, four point diffractors, and addressing issues like bow-tie phenomena through migration techniques.
This document discusses Buckingham's pi-theorem, which states that any physically meaningful relationship between physical quantities can be expressed in terms of dimensionless combinations of those quantities. The document provides an example applying the theorem to the problem of fluid flow through a pipe. Specifically, it shows that the pressure drop through the pipe can be expressed as a function of Reynolds number, relative roughness, and Fanning's friction factor.
This document summarizes a presentation on using the 4th order Runge-Kutta method to model the trajectory of projectiles. It discusses ordinary differential equations, introduces the RK4 method, and applies it to model the trajectory of unguided missiles accounting for gravity and drag forces, as well as guided self-propelled missiles where thrust is also considered. Input parameters for a simulation of a North Korean missile are provided and the optimal range is determined. Limitations of the model and references are also noted.
VariableR jet reclustering is a technique that reconstructs boosted objects like top quarks and W bosons over a wide kinematic range. It does this by varying the radius of reclustering, unlike fixed radius reclustering. When evaluating performance on events with multiple top quarks, VariableR reclustering identifies top quark candidates with masses closer to the actual top quark mass and has a higher reconstruction efficiency than fixed radius reclustering. This enhances sensitivity for searches of new particles that decay into top quarks, like gluinos.
Y. Sitenko: Vacuum Polarization Effects in the Cosmic String Background and P...SEENET-MTP
- The document summarizes research on vacuum polarization effects caused by cosmic strings and primordial magnetic fields in the universe.
- Cosmic strings formed in the early universe through spontaneous symmetry breaking and have properties like linear energy density and inducing vacuum currents that generate magnetic fields.
- Calculations are presented for the induced vacuum energy-momentum tensor in the background of a cosmic string, which depends on the string's properties and the spacetime metric.
- Primordial magnetic fields on galactic or larger scales could have originated from phenomena like superconducting cosmic strings in the early universe.
Neutrino mass is established but its origin is still unknown. The Large Hadron Collider (LHC) may play a crucial role in unraveling the mystery by probing new physics at the TeV scale. LHC could discover the seesaw mechanism responsible for neutrino mass through the detection of new particles like heavy neutrinos. Low-energy neutrino experiments provide complementary information that can be linked to LHC results through precision measurements of neutrino properties. Together, low and high-energy experiments offer an opportunity to understand the origin of neutrino mass.
D01L06 D Tarnita - University of Craiova Steps Towards Interdisciplinary Rese...SEENET-MTP
The document discusses research being conducted at the University of Craiova on modular orthopedic implants using shape memory alloys. The research aims to develop adaptive bone plates made of interchangeable titanium or steel modules connected by nitinol staples. This would allow plates tailored for each bone fracture and enable stabilization, rigidity, and continuous compression needed for healing. Experimental results show these modular implants provide superior osteosynthesis to conventional implants by reducing soft tissue destruction, infections, blood loss, and healing time.
D02L06 D Pavlovic - Educational Outcomes and Policies in Serbia: From Present...SEENET-MTP
Educational outcomes in Serbia are low, with only 4.6% of the population over 15 completing high education and 21.9% not finishing primary school. This results in untapped human capital and high social program spending. There are three main issues - efficacy with low education spending and teacher salaries, equity with high dropout rates and low preschool coverage, and quality with declining test scores far below OECD averages. The document outlines goals from the Lisbon Agenda and EU 2020 to improve these outcomes, such as increasing preschool attendance and tertiary education rates.
This document reviews research on the convergence of perturbation series in quantum field theory. It discusses Dyson's argument that perturbation series in quantum electrodynamics (QED) have zero radius of convergence due to vacuum instability when the coupling constant is negative. Large-order estimates show that perturbation series coefficients grow factorially fast in quantum mechanics and field theories. Finally, it describes the method of Borel summation, which may allow extracting the exact physical quantity from a divergent perturbation series through a unique mapping.
Alexei Starobinsky - Inflation: the present statusSEENET-MTP
This document summarizes a presentation on inflation and the present status of inflationary cosmology. It discusses the key epochs in the early universe, including inflation, and how inflation solved issues with prior models. Observational evidence for inflation is presented, including measurements of the primordial power spectrum and constraints on the tensor-to-scalar ratio. Simple single-field inflation models are shown to match observations. The document also discusses the generation of primordial perturbations from quantum fluctuations during inflation and how this provides the seeds for structure formation.
R. Jimenez: Fundamental Physics Beyond the Standard Model from Astronomical O...SEENET-MTP
This document discusses how future cosmological experiments can provide information about fundamental physics. It summarizes some key findings from the Planck experiment and discusses how measurements of the cosmic microwave background and large scale structure can constrain properties of neutrinos and test for new physics beyond the standard model, such as primordial non-Gaussianities and interactions between photons and axion-like particles. Future surveys like EUCLID are expected to dramatically improve constraints on these models and properties by providing a vast amount of high quality cosmological data.
N. Bilic - "Hamiltonian Method in the Braneworld" 2/3SEENET-MTP
This document discusses braneworld models and the Randall-Sundrum model. It begins by introducing the relativistic particle and string actions used to describe dynamics in higher dimensions. It then summarizes the two Randall-Sundrum models: RS I contains two branes separated in a fifth dimension to address the hierarchy problem, while RS II has the negative tension brane sent to infinity and observers on a single positive tension brane. Finally, it derives the RS II model solution, using Gaussian normal coordinates and imposing junction conditions at the brane.
Nucleation and avalanches in film with labyrintine magnetic domainsAndrea Benassi
This document summarizes a phase field model used to study nucleation and avalanches in films with labyrinthine magnetic domains. The model uses a phase field approach with a power expansion energy functional to simulate the system. It produces two different limit behaviors depending on film thickness and disorder strength: multiple nucleation and coalescence, or expansion by a single branching domain. The model is used to analyze characteristic lengths, domain shapes, and avalanche statistics under variations of parameters like thickness, disorder strength, and temperature. Adding random field and anisotropy terms introduces additional parameters for random field strength and temperature noise.
This document discusses using future full-sky galaxy surveys from space telescopes to probe initial conditions and constrain primordial non-Gaussianity. It proposes launching a space telescope called SPHEREx to conduct a full-sky galaxy spectroscopy survey. This would allow probing the horizon-scale clustering needed to constrain the non-Gaussianity parameter fNL using both the galaxy power spectrum and bispectrum. Current forecasts suggest SPHEREx could achieve an uncertainty of σ(fNL) ~ 0.8 from the power spectrum alone and σ(fNL) ~ 0.2 when also including the bispectrum. However, challenges remain in applying photometric redshift indicators and understanding contributions to the squeezed bispectrum at higher orders.
Alexei Starobinsky "New results on inflation and pre-inflation in modified gr...SEENET-MTP
1. The document summarizes new results on inflation and pre-inflation in modified gravity theories.
2. It discusses the simplest inflationary models in f(R) gravity, where f(R) is a function of the Ricci scalar R. Models with f(R) proportional to R2 can produce inflation.
3. Perturbation spectra during inflation are calculated for slow-roll f(R) models where f(R) is proportional to R2 times a slowly varying function. Scalar and tensor spectra depend on the Ricci scalar and its derivatives evaluated when modes cross the Hubble radius.
1 ECE 6340 Fall 2013 Homework 8 Assignment.docxjoyjonna282
1
ECE 6340
Fall 2013
Homework 8
Assignment: Please do Probs. 1-9 and 13 from the set below.
1) In dynamics, we have the equation
E j Aω= − −∇Φ .
(a) Show that in statics, the scalar potential function Φ can be interpreted as a voltage
function. That is, show that in statics
( ) ( )
B
AB
A
V E dr A B≡ ⋅ = Φ −Φ∫ .
(b) Next, explain why this equation is not true (in general) in dynamics.
(c) Explain why the voltage drop (defined as the line integral of the electric field, as
defined above) depends on the path from A to B in dynamics, using Faraday’s law.
(d) Does the right-hand side of the above equation (the difference in the potential
function) depend on the path, in dynamics?
Hint: Note that, according to calculus, for any function ψ we have
dr dx dy dz d
x y z
ψ ψ ψ
ψ ψ
∂ ∂ ∂
∇ ⋅ = + + =
∂ ∂ ∂
.
2) Starting with Maxwell’s equations, show that the electric field radiated by an impressed
current density source J i in an infinite homogeneous region satisfies the equation
( )2 2 iE k E E j Jωµ∇ + = ∇ ∇⋅ + .
Then use Ampere’s law (or, if you prefer, the continuity equation and the electric Gauss
law) to show that this equation may be written as
( )2 2 1 i iE k E J j J
j
ωµ
σ ωε
∇ + = − ∇ ∇⋅ +
+
.
2
Note that the total current density is the sum of the impressed current density and the
conduction current density, the latter obeying Ohm’s law (J c = σE).
Explain why this equation for the electric field would be harder to solve than the equation
that was derived in class for the magnetic vector potential.
3) Show that magnetic field radiated by an impressed current density source satisfies the
equation
2 2 iH k H J∇ + = −∇× .
Explain why this equation for the magnetic field would be harder to solve than the
equation that was derived in class for the magnetic vector potential.
4) Show that in a homogenous region of space the scalar electric potential satisfies the
equation
2 2
i
v
c
k
ρ
ε
∇ Φ + Φ = − ,
where ivρ is the impressed (source) charge density, which is the charge density that goes
along with the impressed current density, being related by
i ivJ jωρ∇⋅ = −
Hint: Start with E j Aω= − −∇Φ and take the divergence of both sides. Also, take the
divergence of both sides of Ampere’s law and use the continuity equation for the
impressed current (given above) to show that
1 ii v
c c
E J
j
ρ
ωε ε
∇⋅ = − ∇⋅ = .
Note: It is also true from the electric Gauss law that
vE
ρ
ε
∇⋅ = ,
but we prefer to have only an impressed (source) charge density on the right-hand side of
the equation for the potential Φ. In the time-harmonic steady state, assuming a
homogeneous and isotropic region, it follows that ρv = ρvi. That is, there is no charge
3
density arising from the conduction current. (If there were no impressed current sources,
the total charge density would therefore be ze ...
1) The document discusses the challenges in computing the exact CMBR likelihood function due to the large size of the covariance matrix. Approximations like the Gaussian likelihood are generally used.
2) It describes how the Gaussian likelihood is derived under the assumptions of Gaussianity and statistical isotropy of the alm coefficients. The power spectrum estimators contain all the relevant information about the posterior.
3) Maximum likelihood estimation and the Fisher information matrix are discussed as ways to iteratively find the best fit parameters through quadratic estimators without computing the full likelihood at each step.
The Physics of Gas Sloshing in Galaxy ClustersJohn ZuHone
1) The document discusses gas sloshing in galaxy clusters, which occurs when cool core gas is uplifted from the gravitational potential minimum and forms a contact discontinuity with hotter, less dense gas.
2) Simulations of galaxy cluster mergers show that interactions with subclusters can cause gas sloshing by accelerating the gas and dark matter components differently.
3) Observations reveal spiral-shaped cold fronts in galaxy clusters that are evidence of gas sloshing. Magnetic fields may stabilize these fronts by being draped across the interfaces.
While most of the singularities of General Relativity are expected to be safely hidden behind event horizons by the cosmic censorship conjecture, we happen to live in the causal future of the classical big bang singularity, whose resolution constitutes the active field of early universe cosmology...
This document discusses how nonlinear electrodynamics (NLED) may provide a mechanism for forming astrophysical charged black holes during gravitational core collapse supernovae. NLED allows the timescale for charge neutralization in a proto-neutron star to be longer than the gravitational collapse timescale, preventing neutralization and allowing the core to collapse while positively charged. This could result in a charged black hole. The document outlines the theoretical framework of NLED, how it exhibits an inherent repulsive action, and how this could keep the charge separation state of a proto-neutron star stalled long enough for gravitational collapse to occur, forming an astrophysical charged black hole.
Crystal structure determination uses X-ray diffraction to analyze the arrangement of atoms in crystals. X-rays are diffracted by the periodic lattice of a crystal in predictable ways. Bragg's law describes the conditions under which constructive interference occurs between X-rays reflected from different crystal lattice planes, producing intense diffracted beams. By measuring the angles and intensities of these diffracted beams, researchers can determine the size and shape of the unit cell and deduce the positions of atoms within the cell. The reciprocal lattice formalism relates diffraction phenomena to the periodicity of the crystal lattice.
This document discusses uncertainty principles and their application to the double slit experiment. It summarizes Heisenberg's uncertainty principle and its limitations in describing position and momentum spreads. It then applies various uncertainty inequalities to analyze Bohr's argument that an interference pattern requires not knowing which slit particles pass through. Local uncertainty principles assert that low momentum uncertainty implies not only large position uncertainty, but low probability of localization. The document analyzes applying these principles to justify Bohr's response to Einstein's proposed resolution of the double slit ambiguity.
The optimal cosmic_epoch_for_precision_cosmologySérgio Sacani
The document discusses the optimal epoch for precision cosmology measurements based on the number of independent Fourier modes available. It finds that the best constraints on the primordial power spectrum are accessible at redshifts around z=10 through instruments like 21-cm intensity mapping. The ability to constrain the initial cosmological conditions will deteriorate rapidly in our cosmic future as the exponential expansion erases information beyond 100 Hubble times from now.
This document discusses calculating the frequencies of quasinormal modes of black holes using semi-analytical methods. It summarizes that quasinormal modes are oscillations of black holes that emit gravitational waves. The WKB approximation and continued fractions method are used to calculate the frequencies. Results from the WKB method match other semi-analytic results for lower modes. The continued fractions method is also shown to work as another semi-analytic technique.
Braneworld Cosmology and Tachyon Inflation - RSII Numerical ModelsMilan Milošević
This document summarizes a numerical model of tachyon inflation in the context of braneworld cosmology and the Randall-Sundrum II model. The model considers a tachyonic scalar field minimally coupled to gravity on a positive tension brane embedded in an anti-de Sitter bulk. Nondimensional equations are derived and solved numerically. The results show that including the radion field and bulk effects significantly extends the duration of inflation compared to standard tachyon inflation models.
1. The document discusses potential low frequency gravitational wave sources that could be detected by LISA, including galactic white dwarf binaries, massive black hole binaries, and extreme mass ratio inspirals.
2. LISA could detect thousands of massive black hole binaries and provide precise measurements of their parameters like mass and spin, enabling tests of general relativity and learning about black hole formation mechanisms.
3. Extreme mass ratio inspirals where a compact object spirals into a massive black hole could occur at a rate of 10-7 per year in our galaxy, allowing precision cosmology and tests of the no-hair theorem.
Similar to E. Sefusatti, Tests of the Initial Conditions of the Universe after Planck (20)
The document summarizes the Southeastern European Network in Mathematical and Theoretical Physics (SEENET-MTP). It was established in 2003 with participants from several Balkan countries to provide institutional capacity building in mathematical and theoretical physics. It has grown to include over 450 individual members from 15 full network nodes and 8 other network nodes across Southeastern Europe. Over the past 15 years, the SEENET-MTP has realized over 18 projects, held 30 network meetings, facilitated over 300 exchanges, and generated over 225 joint scientific papers and 15 publications. The network continues to promote research collaboration in mathematical and theoretical physics across the region.
Milan Milošević "The shape of Fe Kα line emitted from relativistic accretion ...SEENET-MTP
The document discusses simulations of the Fe Kα emission line from accretion disks around supermassive black holes (SMBHs) in active galactic nuclei (AGN). Ray tracing simulations in Kerr spacetime were used to model the line profiles for different black hole spins, disk radii, inclinations, and emissivity profiles. Relativistic effects like Doppler shifts and gravitational redshift distort the line profiles. Comparisons with observed profiles can determine SMBH properties like mass and spin, providing insights into plasma physics and strong gravity near AGN.
This document discusses nonlocal cosmology and modifications to Einstein's theory of gravity. It presents three cases of nonlocal modified gravity models:
1. When P(R)=R and Q(R)=R, nonsingular bounce cosmological solutions were found with scale factor a(t)=a0(σeλt+τe-λt).
2. When P(R)=R-1 and Q(R)=R, several power-law cosmological solutions were obtained, including a(t)=a0|t-t0|α.
3. For the case P(R)=Rp and Q(R)=Rq, the trace and 00 equations of motion were transformed into an equivalent
Dragoljub Dimitrijević "Tachyon Inflation in the RSII Framework"SEENET-MTP
This document summarizes research on tachyon inflation in an anti-de Sitter (AdS) braneworld framework. The researchers study a tachyon field on a dynamical 3-brane embedded in a 5-dimensional AdS bulk spacetime. They derive the equations of motion for the tachyon field and radion field in this braneworld cosmology. Dimensionless equations are obtained and numerical results show that the model can produce over 60 e-folds of inflation with observable parameters consistent with current data. The analysis provides a novel mechanism for tachyon inflation distinct from standard 4D models, with predictions depending on only one free parameter related to the AdS curvature scale.
Vesna Borka Jovanović "Constraining Scalar-Tensor gravity models by S2 star o...SEENET-MTP
This document summarizes research that uses observations of S-star orbits around the Galactic Center to constrain scalar-tensor gravity models. The authors simulate orbits of the S2 star in scalar-tensor potentials and compare them to observations. They find that certain scalar-tensor parameters produce a better fit to the observed S2 star orbit than Newtonian gravity. In particular, they identify ranges of scalar-tensor coupling constants and self-interaction strengths that are consistent with the orbital precession and trajectory of S2. This allows them to test scalar-tensor theories of gravity using stellar dynamics near the Galactic Center.
Elena Mirela Babalic "Generalized alpha-attractor models for hyperbolic surfa...SEENET-MTP
This document discusses generalized two-field α-attractor models of inflation where the scalar manifold is any hyperbolic surface rather than just the Poincaré disk. It introduces uniformization techniques to study trajectories on such surfaces by lifting them to the Poincaré half-plane and projecting back. Near the ends of non-compact surfaces, trajectories typically follow spiral paths around ideal points. The document focuses on geometrically finite hyperbolic surfaces and potentials that are well-behaved at the ends.
Mihai Visinescu "Action-angle variables for geodesic motion on resolved metri...SEENET-MTP
This document discusses complete integrability on various geometries related to the Sasaki-Einstein space T1,1:
1. The geodesic flow on T1,1 space itself is completely integrable, with the Hamiltonian depending on conjugate momenta and conserved quantities like total angular momenta.
2. On the metric cone over T1,1, the geodesic flow separates into independent radial and angular parts. The angular part can be formulated using action-angle variables while the radial part involves unbounded motion.
3. For the resolved metric cone, which involves deformations or resolutions of the conical singularity, the complete integrability structure carries over by extending the action-angle
Sabin Stoica "Double beta decay and neutrino properties"SEENET-MTP
Double beta decay and its potential to explore beyond Standard Model physics was summarized. Double beta decay is the rarest nuclear decay measured, where a nucleus transforms into another nucleus with the same mass but a change of two units in nuclear charge. It can occur even if single beta decay is forbidden. There are two types of double beta decay processes - two neutrino double beta decay (2νββ) and neutrinoless double beta decay (0νββ). 0νββ decay has the potential to provide information about neutrino properties like mass hierarchy and explore beyond Standard Model physics by constraining parameters associated with different mechanisms that could contribute to 0νββ. Challenges include accurately calculating nuclear matrix elements and reducing background in experiments searching
Yurri Sitenko "Boundary effects for magnetized quantum matter in particle and...SEENET-MTP
This document discusses boundary conditions for quantized spinor matter fields and their impact on physical systems. It proposes a general boundary condition for spinor fields that ensures the self-adjointness of the Dirac Hamiltonian operator. This boundary condition confines the spinor matter inside spatial boundaries. The condition reduces to the MIT bag boundary condition in a specific case. Quantized spinor fields obeying this boundary condition can be used to study phenomena in hot dense magnetized matter found in particle physics and astrophysics.
Predrag Milenović "Physics potential of HE/HL-LHC and future circular"SEENET-MTP
The document discusses latest Higgs boson physics results from the LHC and prospects for physics performance at the HL-LHC. Key results presented include measurements of the Higgs boson mass, production cross sections and branching ratios using H→4l and H→γγ decay channels. Differential measurements are also shown. First direct evidence is reported for ttH production in multilepton final states with a significance of 3.3σ. The increased luminosity of the HL-LHC is expected to improve measurements and search sensitivity.
Marija Dimitrijević Ćirić "Matter Fields in SO(2,3)⋆ Model of Noncommutative ...SEENET-MTP
This document summarizes a talk given at a workshop on field theory and the early universe. The talk discussed a model of noncommutative gravity based on an SO(2,3) gauge theory. Key points:
1) The model treats gravity as an SO(2,3) gauge theory that is spontaneously broken to SO(1,3), relating it to general relativity. An action is constructed and expanded to obtain corrections from noncommutativity.
2) Adding matter fields like spinors and U(1) gauge fields yields modified actions and propagators with corrections depending on the noncommutativity tensor.
3) As an example, the noncommutative Landau problem is solved, giving
Zvonimir Vlah "Lagrangian perturbation theory for large scale structure forma...SEENET-MTP
This document discusses using Lagrangian perturbation theory and the effective field theory (EFT) approach to model large-scale structure (LSS) formation, including nonlinear effects. Key points include:
- The Lagrangian framework tracks fluid elements as they move due to gravity, described by a displacement field. This allows modeling of shell crossing nonlinearities.
- The EFT approach introduces a stress tensor to account for short-distance effects on long-wavelength modes. Counterterms are included to absorb uncertainties from neglected short-scale physics.
- Power spectrum and correlation function results from the Lagrangian EFT approach match those of the standard Eulerian EFT approach. The Lagrangian approach provides insights into counterterm structures and infrared resummation
Vitaly Vanchurin "General relativity from non-equilibrium thermodynamics of q...SEENET-MTP
1) The document proposes that general relativity can emerge from quantum mechanics in the limit of many degrees of freedom, similar to how thermodynamics emerges from classical mechanics with many particles.
2) It suggests defining statistical ensembles over wave functions using an "infoton field" to obtain a spatially covariant description of quantum information, represented by an information tensor.
3) A dual theory description of computational complexity is developed using the infoton field, arriving at a Klein-Gordon theory with an inverse metric related to computational parameters like the number of qubits. This provides a space-time covariant description of quantum computation.
Sergey Sibiryakov "Galactic rotation curves vs. ultra-light dark matter: Impl...SEENET-MTP
The document discusses ultra-light dark matter and its implications for galactic rotation curves. It begins by providing theoretical background on ultra-light dark matter and how it can form soliton cores within dark matter halos. It then discusses how the properties of these soliton cores, such as their mass and size, relate to the properties of the ultra-light dark matter particle. Finally, it discusses how measurements of galactic rotation curves could provide insights into ultra-light dark matter models by probing the presence and characteristics of these soliton cores.
Radoslav Rashkov "Integrable structures in low-dimensional holography and cos...SEENET-MTP
This document outlines R.C. Rashkov's presentation on integrable structures in low-dimensional holography and cosmology. The presentation covers several topics: (1) the Möbius structure of entanglement entropy and its relation to dispersionless Toda hierarchies, (2) holographic entanglement entropy of excited states, (3) higher spin holography and higher projective invariants, and (4) bulk reconstruction and its consequences. The presentation also discusses conceptual issues regarding the duality between gravity/string theories and gauge theories, such as how information is encoded in the boundary theory and whether spacetime and gravity can emerge from a boundary theory.
Nikola Godinović "The very high energy gamma ray astronomy"SEENET-MTP
This document discusses using gamma-ray astronomy to study fundamental physics. It outlines how gamma-ray telescopes like IACT arrays and satellites are used to search for dark matter by looking for gamma rays from annihilation. Combining data from Fermi and IACTs like MAGIC improves sensitivity to constrain dark matter models. No evidence of dark matter has been found so far, but future instruments like CTA will provide stronger limits. The document also mentions how gamma-ray observations can probe Lorentz invariance violation and the origin of cosmic rays.
Miroljub Dugić "The concept of Local Time. Quantum-mechanical and cosmologica...SEENET-MTP
This document discusses the concept of local time from quantum mechanical and cosmological perspectives. It provides a historical overview, discussing Schrodinger's work developing the nonstationary wave equation and Hitoshi Kitada's view that both equations are valid when time is altered. The document then examines the Enss' theorem, which establishes a link between time and Hamiltonian through the dynamical evolution of a system. This leads to a new reading of the Enss' theorem and concept of local time - that time is dynamically generated for each system based on its Hamiltonian. Basic elaborations explore properties of local time, including its inherent uncertainty and role in quantum dynamics.
Cemsinan Deliduman "Astrophysics with Weyl Gravity"SEENET-MTP
This document summarizes a presentation on astrophysical aspects of Weyl gravity. It discusses how Weyl gravity may help explain galaxy rotation curves without dark matter by having the Einstein-Hilbert term dominate in the inner region and the Weyl term dominate in the outer region. It also examines gravitational lensing predictions in Weyl gravity. Future directions are proposed such as matching interior and exterior solutions, investigating scale invariance breaking, and applications to other astrophysical problems.
Radu Constantinescu "Scientific research: Excellence in International context"SEENET-MTP
The University of Craiova is located in Craiova, Romania and was founded in 1947. It has over 16,000 students studying across 16 faculties, with the most popular being sciences, economics, and engineering. The university focuses its research efforts on nanosciences, information technology, energy, environment, transport, food and agriculture, and social sciences. It also operates a research hub called INCESA to foster cooperation with industry.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
E. Sefusatti, Tests of the Initial Conditions of the Universe after Planck
1. Emiliano Sefusatti
Tests of the Initial Conditions of the Universe after Planck
BW2013,Vrnjačka Banja
April 27th, 2013
2. Outline
• Initial Conditions from Inflation
• CMB Constraints
• Implications of Planckʼs results (a sample)
• Beyond fNL
• Prospects for Large-Scale Structure Observations
• Conclusions
3. Predictions of Inflation
• A flat, homogeneous Universe
PLANCK (2013)
Planck Collaboration: The Planck mission
Fig. 14. The SMICA CMB map (with 3 % of the sky replaced by a constrained Gaussian realization).
4. Predictions of Inflation
Planck Collaboration: Cosmological parameters
• A flat, homogeneous Universe
• A (nearly) scale invariant power spectrum for (highly Gaussian) initial fluctuations
PLANCK (2013)
5. Predictions of Inflation
• A flat, homogeneous Universe
• A (nearly) scale invariant power spectrum for (highly Gaussian) initial fluctuations
Φk1
Φk2
= δD(k1 +k2)PΦ(k1)
Φk1
Φk2
Φk3
Φk4
= δD(k1 + ... +k4) TΦ(k1,k2,k3,k4) = 0
Φk1
Φk2
Φk3
= δD(k1 +k2 +k3) BΦ(k1, k2, k3) = 0
6. Assumptions for a simple inflation model
• A single, weakly coupled scalar field
• with canonical kinetic term
• slow rolling down a smooth potential
• initially in a Bunch-Davies vacuum
7. Assumptions for a simple inflation model
• A single, weakly coupled scalar field
• with canonical kinetic term
• slow rolling down a smooth potential
• initially in a Bunch-Davies vacuum
8. Assumptions for a simple inflation model
• A single, weakly coupled scalar field
• with canonical kinetic term
• slow rolling down a smooth potential
• initially in a Bunch-Davies vacuum
9. Assumptions for a simple inflation model
• A single, weakly coupled scalar field
• with canonical kinetic term
• slow rolling down a smooth potential
• initially in a Bunch-Davies vacuum
10. Assumptions for a simple inflation model
• A single, weakly coupled scalar field
• with canonical kinetic term
• slow rolling down a smooth potential
• initially in a Bunch-Davies vacuum
BΦ(k1, k2, k3) = 0
TΦ(k1,k2,k3,k4) = 0
Non-Gaussian Initial Conditions
11. The shape of non-Gaussianity
Most models predict a scale-invariant curvature bispectrum
BΦ(k, k, k) ∼ P2
Φ(k) ∼
1
k6
What distinguish them is the shape
“shape” = the dependence of the curvature bispectrum predicted
by a given model of inflation on the shape of the triangular
configuration k1, k2, k3
BΦ(k1, k2, k3) = fNL
1
k2
1k2
2k2
3
F
r2 =
k2
k1
, r3 =
k3
k1
12. Models of primordial non-Gaussianity
Multiple fields
Modified vacuum
Modified vacuum
Non-Canonical
Kinetic term
14. The CMB Bispectrum
The Bispectrum of the CMB is the most
direct probe of the initial bispectrum
Bl1l2l3
∼
BΦ(k1, k2, k3)∆l1
(k1)∆l2
(k2)∆l3
(k3)jl1
(k1r)jl2
(k2r)jl3
(k3r)
curvature
bispectrum
transfer
functions
CMB angular
bispectrum
WMAP 7 years:
Local -10 fNL 74
Equilateral -214 fNL 266
Orthogonal -410 fNL 6
@ 95% CL Komatsu et al. (2009)
• The CMB provides a snapshot of density perturbations at early times
• Power spectrum measurements (Clʼs) are matched by linear predictions
• The CMB bispectrum is equally sensitive to any model of non-Gaussianity
15. The CMB Bispectrum
The Bispectrum of the CMB is the most
direct probe of the initial bispectrum
Bl1l2l3
∼
BΦ(k1, k2, k3)∆l1
(k1)∆l2
(k2)∆l3
(k3)jl1
(k1r)jl2
(k2r)jl3
(k3r)
curvature
bispectrum
transfer
functions
CMB angular
bispectrum
WMAP 7 years:
Local -10 fNL 74
Equilateral -214 fNL 266
Orthogonal -410 fNL 6
@ 95% CL Komatsu et al. (2009)
• The CMB provides a snapshot of density perturbations at early times
• Power spectrum measurements (Clʼs) are matched by linear predictions
• The CMB bispectrum is equally sensitive to any model of non-Gaussianity
Planck (T only):
Local -8.9 fNL 14.3
Equilateral -192 fNL 108
Orthogonal -103 fNL 53
@ 95% CL Ade et al. (2013)
16. The CMB Bispectrum: Planck
• Planck temperature data improve WMAP
results by a factors of 2 to 4 (depending on
the shape!)
• Planck is very close to the
ideal CMB experiment (ΔfNLlocal ~ 1)
ΔfNL, local ΔfNL, equil. ΔfNL, orth.
WMAP 21 140 104
Planck 5.8 75 39
17. The CMB Bispectrum: Planck
dvances in Astronomy 2
1
2
3
4
5
10
20
∆fNL
200 300 500 700 1000 1500 2000 3000
Local model
Imax
WMAP (T/T+P)
Planck (T/T+P)
CMBPol (T/T+P)
(a)
20
30
40
50
100
∆fNL
200 300 500 700 1000 1500 2000 3000
Equilateral model
Imax
WMAP (T/T+P)
Planck (T/T+P)
CMBPol (T/T+P)
(b)
• Planck temperature data improve WMAP
results by a factors of 2 to 4 (depending on
the shape!)
• Planck is very close to the
ideal CMB experiment (ΔfNLlocal ~ 1)
Liguori et al. (2010)
ΔfNL, local ΔfNL, equil. ΔfNL, orth.
WMAP 21 140 104
Planck 5.8 75 39
Forecasted
temperature
polarization
constraints
18. Implications of Planck’s results: an example
DBI inflation (IR)
Having characterised single-field inflation bispectra using com-
binations of the separable equilateral and orthogonal ans¨atze
we note that the actual leading-order non-separable contribu-
tions (Eqs. (6, 7)) exhibit significant differences in the collinear
(flattened) limit. For this reason we provide constraints on DBI
inflation (Eq. (7)) and the two effective field theory shapes
(Eqs. (5, 6)), as well as the ghost inflation bispectrum, which
is an exemplar of higher-order derivative theories (specifically
Eq. (3.8) in Arkani-Hamed et al. 2004). Using the primordia
modal estimator, with the SMICA foreground-cleaned data, we
find:
fDBI
NL = 11 ± 69 (F
DBI−eq
NL = 10 ± 77) ,
fEFT1
NL = 8 ± 73 (F
EFT1−eq
NL = 8 ± 77) ,
fEFT2
NL = 19 ± 57 (F
EFT2−eq
NL = 27 ± 79) ,
fGhost
NL = −23 ± 88 (F
Ghost−eq
NL = −20 ± 75) . (86)
where we have normalized with the usual primordial f con-
where ds2
4 g dx dx is the metric of the four-
dimensional space-time and is a dimensionless parame-
ter. The inflaton and the parameter are related to the
notations of Refs. [3,4] by r T3
p
and T3R4 N.
The has the same order of magnitude as the effective
background charge N of the warped space and character-
izes the strength of the background. The low-energy dy-
namics is described by the DBI–Chern-Simons action
S
M2
Pl
2
Z
d4
x g
p
R
Z
d4
x g
p 4
1 4
g @ @
s
4
V : (2.3)
In the nonrelativistic limit, this action reduces to the usual
minimal form.
We start the inflaton near 0 through a phase tran-
sition.1
Without the warped space, the scalar will quickly
roll down the steep potential ( * 1) and make the infla-
t comes from backreactions of the
[1,4,9] and the de Sitter (dS) space
space. These effects will smooth out th
of a certain IR region of the warped sp
if we start the inflaton from that reg
period cannot be further increased in t
magnitude. For the case that we consi
gest lower bound is the closed string c
background. This gives t
p
H 1
number of e-foldings in this model i
latest e-fold Ne is given by
Ne
p
H= :
It has an interesting relation to the
factor of the inflaton,
Ne=3:
Since the sound speed cs
1, durin
1
This initial condition can be naturally obtained without tun-
ing in e.g. a scenario of Refs. [3,4].
2
This corresponds to the case of a single
throat in Refs. [3,4].
3
So we cannot use the results of Ref. [1
tion has been made that cs departs from un
less than one.
notations of Refs. [3,4] by r T3
p
and T3R4 N.
The has the same order of magnitude as the effective
background charge N of the warped space and character-
izes the strength of the background. The low-energy dy-
namics is described by the DBI–Chern-Simons action
S
M2
Pl
2
Z
d4
x g
p
R
Z
d4
x g
p 4
1 4
g @ @
s
4
V : (2.3)
In the nonrelativistic limit, this action reduces to the usual
minimal form.
We start the inflaton near 0 through a phase tran-
sition.1
Without the warped space, the scalar will quickly
roll down the steep potential ( * 1) and make the infla-
space. These effect
of a certain IR regio
if we start the infl
period cannot be fu
magnitude. For the
gest lower bound is
background. This
number of e-foldin
latest e-fold Ne is g
It has an interestin
factor of the inflato
Since the sound spe
1
This initial condition can be naturally obtained without tun-
ing in e.g. a scenario of Refs. [3,4].
2
This corresponds
throat in Refs. [3,4].
3
So we cannot use
tion has been made th
less than one.
123518-2
background charge N of the warped sp
izes the strength of the background. T
namics is described by the DBI–Chern
S
M2
Pl
2
Z
d4
x g
p
R
Z
d4
x g
p 4
1 4
g
s
4
V :
In the nonrelativistic limit, this action r
minimal form.
We start the inflaton near 0 thr
sition.1
Without the warped space, the
roll down the steep potential ( * 1) a
1
This initial condition can be naturally o
ing in e.g. a scenario of Refs. [3,4].
s improvements, may come at least in two occasions
—where the redshifted string scale is too low so that
gy effects become significant or where the relativistic
ating is happening in a relatively deep warped space so
cosmological rescaling [9] takes effect. We discuss the
in Sec. IV.
II. THE IR MODEL
this section, we study the non-Gaussianity in the
plest IR DBI inflation model. We begin with a brief
ew on the model. Details can be found in Refs. [3,4].
he inflaton potential is parametrized as
V V0
1
2m2 2
V0
1
2 H2 2
; (2.1)
re the Hubble parameter H is approximately a con-
t. In many inflationary models, there is always natu-
a contribution to the potential with j j 1. In these
els, such a potential is too steep to support a long
od of slow-roll inflation. This is the well-known
lem which plagues slow-roll inflation [10].
owever, it is shown [4] that, with warped space, the
inflation can happen for both small and large
t generates a scale-invariant spectrum for the density
urbations with a tilt independent of the parameter . In
case, the steepness of the potential does not play such
mportant role. The inflaton stays on the potential due to
arping in the internal space
tion impossible. To obtain inflation, it is natural to e
that the speed limit should be nearly saturated. In
solving the equations of motion, we find
p
t
9
p
2 2
H2
1
t3
; t H 1
;
where the time t is chosen to run from 1. The in
travels ultrarelativistically with a Lorentz contractio
tor
1 _ 2
= 4 1=2:
Nonetheless, the coordinate speed of light is very sma
to the large warping near 0, and in such a wa
inflaton achieves ‘‘slow rolling.’’ The potential stays n
constant during the inflation, and we have a peri
exponential expansion with the Hubble constant
_a=a V0
p
= 3
p
MPl. There is no lower bound on the
tionary scale, and the approximations that H is co
and dominated by the potential energy during infl
require an upper bound on V [4],
V
M4
Pl
1
Ne
:
Generally speaking, this bound is not significant, sin
get enough e-foldings, we need only * 104. How
for some specific models, such as the simplest one th
focus on in this paper, is determined by density p
As shown in Table 21
ndard deviation shows
asets. That means that
ant, as they do not bias
t increase the variance
MB primordial signal.
l
− fclean
NL on a map-by-
ion. This is used as an
realization due to the
ed from the negligible
wo samples, the vari-
o very small: Table 21
6 for any given shape,
for that shape. As an
ed values of flocal
NL for
ILC samples, compar-
evident also from this
including residuals is
ween the two compo-
ice.
m the comparison be-
hods in Sect. 7, we can
eground-cleaned maps
n this work provide a
s
The DBI class contains two possibilities based on string con-
structions. In ultraviolet (UV) DBI models, the inflaton field
moves under a quadratic potential from the UV side of a warped
background to the infrared side. It is known that this case is al-
ready at odds with observations, if theoretical internal consis-
tency of the model and constraints on power spectra and primor-
dial NG are taken into account (Baumann McAllister 2007;
Lidsey Huston 2007; Bean et al. 2007; Peiris et al. 2007). Our
results strongly limit the relativistic r´egime of these models even
without applying the theoretical consistency constraints.
It is therefore interesting to look at infrared (IR) DBI mod-
els (Chen 2005b,a) where the inflaton field moves from the IR to
the UV side, and the inflaton potential is V(φ) = V0 − 1
2 βH2
φ2
,
with a wide range 0.1 β 109
allowed in principle. In
previous work (Bean et al. 2008) a 95% CL limit of β 3.7
was obtained using WMAP. In a minimal version of IR DBI,
where stringy effects are neglected and the usual field the-
ory computation of the primordial curvature perturbation holds,
one finds (Chen 2005c; Chen et al. 2007b) cs (βN/3)−1
,
ns − 1 = −4/N, where N is the number of e-folds; further,
primordial NG of the equilateral type is generated with an
amplitude fDBI
NL = −(35/108) [(β2
N2
/9) − 1]. For this model,
the range N ≥ 60 is compatible with Planck’s 3σ limits on
ns (Planck Collaboration XXII 2013). Marginalizing over 60 ≤
43
Planck Collaboration: Pl
N ≤ 90, we find
β ≤ 0.7 95% CL ,
dramatically restricting the allowed parameter s
model.
Power-law k-inflation: These models (Armendariz
1999; Chen et al. 2007b) predict f
equil
NL = −170/(
(non-canonical kinetic term)
Constraints on the amplitude
of the predicted bispectrum
Constraints on the model parameters
19. Effective Field Theory of Inflation
Cheung et al. 2008) provides a general way to scan the NG pa-
rameter space of inflationary perturbations. For example, one
can expand the Lagrangian of the dynamically relevant degrees
of freedom into the dominant operators satisfying some under-
lying symmetries. We will focus on general single-field models
parametrized by the following operators (up to cubic order)
S =
d4
x
√
−g
−
M2
Pl
˙H
c2
s
˙π2
− c2
s
(∂iπ)2
a2
(97)
− M2
Pl
˙H(1 − c−2
s )˙π
(∂iπ)2
a2
+
M2
Pl
˙H(1 − c−2
s ) −
4
3
M4
3
˙π3
where π is the scalar degree of freedom (ζ = −Hπ). The mea-
surements on f
equil
NL and fortho
NL can be used to constrain the mag-
nitude of the inflaton interaction terms ˙π(∂iπ)2
and (˙π)3
which
give respectively fEFT1
NL = −(85/324)(c−2
s − 1) and fEFT2
NL =
−(10/243)(c−2
s − 1)
˜c3 + (3/2)c2
s
(Senatore et al. 2010, see also
Chen et al. 2007b; Chen 2010b). These two operators give rise
to shapes that peak in the equilateral configuration that are,
nevertheless, slightly different, so that the total NG signal will
be a linear combination of the two, possibly leading also to
an orthogonal shape. There are two relevant NG parameters,
cs, the sound speed of the the inflaton fluctuations, and M3
which characterizes the amplitude of the other operator ˙π3
.
10−2
−2000
Fig. 23. 68%, 95
field inflation pa
the change of va
Following Senat
less parameter ˜c
inflationary mod
non-interacting m
M3 = 0 (or ˜c3(c−
s
The mean va
onal NG amplitu
f
equil
NL =
1 − c2
s
c2
s
(
fortho
NL =
1 − c2
s
c2
s
(
eld Theory of Inflation
ch to inflation (Weinberg 2008;
eneral way to scan the NG pa-
erturbations. For example, one
e dynamically relevant degrees
perators satisfying some under-
on general single-field models
perators (up to cubic order)
c2
s
(∂iπ)2
a2
(97)
M2
Pl
˙H(1 − c−2
s ) −
4
3
M4
3
˙π3
reedom (ζ = −Hπ). The mea-
n be used to constrain the mag-
terms ˙π(∂iπ)2
and (˙π)3
which
5/324)(c−2
s − 1) and fEFT2
NL =
(Senatore et al. 2010, see also
These two operators give rise
ilateral configuration that are,
o that the total NG signal will
two, possibly leading also to
two relevant NG parameters,
inflaton fluctuations, and M3
3
10−2 10−1 100
cs
−20000−
Fig. 23. 68%, 95%, and 99.7% confidence regions in the single-
field inflation parameter space (cs, ˜c3), obtained from Fig. 22 via
the change of variables in Eq. (98).
Following Senatore et al. (2010) we will focus on the dimension-
less parameter ˜c3(c−2
s − 1) = 2M4
3c2
s /( ˙HM2
Pl). For example, DBI
inflationary models corresponds to ˜c3 = 3(1 − c2
s )/2, while the
non-interacting model (vanishing NG) correspond to cs = 1 and
M3 = 0 (or ˜c3(c−2
s − 1) = 0).
The mean values of the estimators for equilateral and orthog-
onal NG amplitudes are given in terms of cs and ˜c3 by
f
equil
NL =
1 − c2
s
c2
s
(−0.275 + 0.0780A)
fortho
NL =
1 − c2
s
(0.0159 − 0.0167A) (98)
one scalar DF
e Field Theory of Inflation
proach to inflation (Weinberg 2008;
a general way to scan the NG pa-
y perturbations. For example, one
of the dynamically relevant degrees
nt operators satisfying some under-
ocus on general single-field models
g operators (up to cubic order)
π2
− c2
s
(∂iπ)2
a2
(97)
+
M2
Pl
˙H(1 − c−2
s ) −
4
3
M4
3
˙π3
of freedom (ζ = −Hπ). The mea-
can be used to constrain the mag-
ction terms ˙π(∂iπ)2
and (˙π)3
which
−(85/324)(c−2
s − 1) and fEFT2
NL =
2)c2
s
(Senatore et al. 2010, see also
0b). These two operators give rise
equilateral configuration that are,
nt, so that the total NG signal will
10−2 10−1
cs
−20000−10
˜c3
Fig. 23. 68%, 95%, and 99.7% confidence regions in th
field inflation parameter space (cs, ˜c3), obtained from Fi
the change of variables in Eq. (98).
Following Senatore et al. (2010) we will focus on the dim
less parameter ˜c3(c−2
s − 1) = 2M4
3c2
s /( ˙HM2
Pl). For exam
inflationary models corresponds to ˜c3 = 3(1 − c2
s )/2, w
non-interacting model (vanishing NG) correspond to cs
M3 = 0 (or ˜c3(c−2
s − 1) = 0).
The mean values of the estimators for equilateral an
onal NG amplitudes are given in terms of cs and ˜c3 by
equil 1 − c2
s
Equilateral -192 fNL 108
Orthogonal -103 fNL 53
S = d4
x
√
−g
−
M2
Pl
˙H
c2
s
˙π2
− c2
s
(∂iπ)2
a2
− M2
Pl
˙H(1 − c−2
s )˙π
(∂iπ)2
a2
+
M2
Pl
˙H(1 − c
where π is the scalar degree of freedom (ζ
surements on f
equil
NL and fortho
NL can be used t
nitude of the inflaton interaction terms ˙π(∂
give respectively fEFT1
NL = −(85/324)(c−2
s
−(10/243)(c−2
s − 1)
˜c3 + (3/2)c2
s
(Senatore
Chen et al. 2007b; Chen 2010b). These two
to shapes that peak in the equilateral co
nevertheless, slightly different, so that the
be a linear combination of the two, poss
an orthogonal shape. There are two relev
cs, the sound speed of the the inflaton fl
which characterizes the amplitude of the
44
Implications of Planck’s results: an example
22. Beyond fNL
Running non-Gaussianity
A scale-dependent fNL
2 parameters:
amplitude (fNL) and running (nNG)
fNL(k) = fNL
k
kP
nNG
The level of non-Gaussianity could
be different at different scales
sh
a
on
us
w
pr
m
la
co
an
ta
Lo Verder et al. (2008), ES, Liguori, Yadav, Jackson, Pajer (2009)
Becker Huterer (2009) from WMAP data
23. Beyond fNL
The PLANCK analysis considered several models
• Feature and resonant models
• Non Bunch-Davies vacuum
• Quasi-single field inflation
• et al.
• + some preliminary tests of the initial trispectrum
No evidence so far!
However ...
!#$
#% #% ##% #% '##% '#% (##%
)*+,%0345,6%
Fig. 8. Modal bispectrum coefficients βR
n for the mode expansion
(Eq. (63)) obtained from Planck foreground-cleaned maps using
hybrid Fourier modes. The different component separation meth-
ods, SMICA, NILC and SEVEM exhibit remarkable agreement. The
variance from 200 simulated noise maps was nearly constant for
each of the 300 modes, with the average ±1σ variation shown in
red.
!!#$!!#%!!#!!#'!!#
!# (!!# $!!# )!!# %!!# *!!# !!#
+,-./01,#234
$#
567,#89:;,#!
!3=4
#?@A@5
#?5=B
(orthonormal basis for the primordial bispectrum)
25. From the CMB to the Large-Scale Structure
No direct access to
matter perturbations ...
... but a large volume
to explore, with several
observables:
1. galaxies
2. weak lensing
3. clusters
4. Ly-alpha forest
5. 21 cm (?)
Predictions are
challenging!
26. The Matter Power Spectrum
matter overdensity: δm ≡
ρm(x) − ¯ρm
¯ρm
δk1
δk2
≡ δD(k1 + k2) Pm(k1)
0.01 0.1 1 10
0.01
1
100
k h Mpc1
k4ΠPkk3
Nbody
nonlinear
linear
matter power spectrum
27. 0.01 0.1 1 10
0.01
1
100
k h Mpc1
k4ΠPkk3
Nbody
nonlinear
linear
TextLarge scales:
initial conditions, inflation
matter overdensity: δm ≡
ρm(x) − ¯ρm
¯ρm
δk1
δk2
≡ δD(k1 + k2) Pm(k1)
matter power spectrum
The Matter Galaxy Power Spectrum
Pg(k) b2
Pm(k)
galaxy power spectrum
28. fNL = - 5000
fNL = - 500
fNL = + 500
fNL = + 5000
Ωm 0.271+0.005
−0.004 0.271+0.001
−0.001
σ8 0.808+0.005
−0.005 0.808+0.003
−0.003
h 0.703+0.004
−0.004 0.703+0.001
−0.001
0.96 0.965 0.97 0.975
!0.01
0
0.01
ns
s
Planck + EUCLID
Planck
0.26 0.27
0.79
0.8
0.81
0.82
#m
$8
Plan
Plan
Figure 3.1: The marginalized likelihood contours (68.3% and 95.4% CL) for Pla
The Galaxy Power Spectrum
Forecasted constraints on
spectral index and its running
for EUCLID
Amendola et al. (2012)
Constraints on the initial power spectrum:
29. The Galaxy Power Spectrum
using the halo auto spectra to compute
results as the cross spectra; i.e. we
stochasticity. Examples of the variou
resulting bias factors are plotted in F
As can be seen, we numerically co
predicted scale dependence. Becau
statistics of rare objects, the errors on
simulations plotted in Fig. 8 are lar
tempt to improve the statistics on the
bining the bias measurements from
Figure 8 plots the average ratio betwe
in our simulations and our analytic
using c ¼ 1:686 as predicted from t
model [78]. In computing the average
we used a uniform weighting across
IMPRINTS OF PRIMORDIAL NON-GAUSSIANITIES ON . . . PHYSICAL REVIEW
The bias of galaxies receives a
significant scale-dependent
correction for NG initial
conditions of the local type
Dalal et al. (2008)
“Gaussian”
bias
Scale-dependent correction
due to local non-Gaussianity
Large effect on large scales!
Pg(k) = [b1 + ∆b1(fNL, k)]2
P(k)
∆b1,NG(fNL, k) ∼
fNL
D(z) k2
Constraints on the initial bispectrum:
30. CMB WMAP (95% CL): -10 fNL 74
[WMAP7, Komatsu et al. (2009)]
QSOs (95% CL): -31 fNL 70
[SDSS, Slosar et al. (2008)]
AGNs (95% CL): 25 fNL 117
[NVSS, Xia et al. (2010)]
Limits from LSS are competitive with the CMB!
(at least for the local model ...)
The Galaxy Power Spectrum
Pg(k) = [b1 + ∆b1(fNL, k)]2
P(k)
The bias of galaxies receives a
significant scale-dependent
correction for NG initial
conditions of the local type
Constraints on the initial bispectrum:
31. CMB WMAP (95% CL): -10 fNL 74
[WMAP7, Komatsu et al. (2009)]
QSOs (95% CL): -31 fNL 70
[SDSS, Slosar et al. (2008)]
AGNs (95% CL): 25 fNL 117
[NVSS, Xia et al. (2010)]
Limits from LSS are competitive with the CMB!
(at least for the local model ...)
The Galaxy Power Spectrum
Pg(k) = [b1 + ∆b1(fNL, k)]2
P(k)
CMB PLANCK (95% CL): -8.9 fNL 14.3
[PLANCK (2013)]?
EUCLID/LSST (95% CL): ΔfNL 5 (~1?), expected!
[Carbone et al. (2010), Giannantonio et al. (2012)]
The bias of galaxies receives a
significant scale-dependent
correction for NG initial
conditions of the local type
Constraints on the initial bispectrum:
32. The Galaxy Bispectrum
Future, large volume surveys
could provide:
ΔfNL
local ~ 5 and ΔfNL
eq ~ 10
i.e. competitive constraints
for all types of non-Gaussianity
ES Komatsu (2007), ES, Crocce Desjacques (2012)
The galaxy 3-point function is the
natural equivalent of the CMB
bispectrum
Bgal b3
1 [Binitial + Bgravity] + b2
1 b2 P2
m
33. 0.02 0.04 0.06 0.08 0.10
5
10
20
50
100
kmax h Mpc1
fNL
V 10 h3
Gpc3
, z 1
kmin 0.009 h Mpc1
b1 2, b2 0.8
P
B
PB
FIG. 15: One-σ uncertainty on the fNL parameter, mar
A Fisher matrix analysis for Galaxy correlators
The uncertainty on fNL (local)
from Power Spectrum
Bispectrum ( both)
marginalized (b1, b2)
34. • Abundance of galaxy clusters
Other probes
PNG affects the high-mass tail
of the cluster mass function
2 Williamson, et al.
10
SZ M500 (1014
Msol /h70)
1
10
LX/E(z)1.85
(1044
ergs-1
h70
-2
;0.5-2.0keV)
Fig. 4.— The X-ray luminosity and SZ inferred masses
500(ρcrit) for our cluster sample. We plot statistical uncertainties
ly, and note that the statistical uncertainty of the SZ mass esti-
ate is limited by the assumed scatter in the SZ significance-mass
ation. Clusters from the shallow fields are in blue, and clusters
m the deep fields are in red. We also show the best-fit relations
Pratt et al. (2009) (dotted), Vikhlinin et al. (2009a) (dash-dot),
d Mantz et al. (2010) (dashed).
ost massive galaxy clusters in this region of the sky,
dependent of the cluster redshift. These exceedingly
Fig. 5.— A Mortonson et al. (2010)-style plot showing the mass
M200(ρmean) and redshift of the clusters presented in this paper.
Some of the most extreme objects in the catalog are annotated with
the R.A. portion of their object name. The red solid line shows
the mass above which a cluster at a given redshift is less than
5% likely to be found in the 2500 deg2 SPT survey region in 95%
of the ΛCDM parameter probability distribution. The black dot-
dashed line shows the analogous limit for the full sky. The blue
open data point (redshift slightly offset for clarity) denotes the
mass estimate for SPT-CL J2106-5844 from combined X-ray and
SZ measurements in Foley et al. (2011). That work concludes that
this cluster is less than 5% likely in 32% of the ΛCDM parameter
probability distribution, and we show the corresponding Mortonson
Williamson et al. (2011)
Sample of the most
massive clusters in the
SPT catalog vs the
“probability of their
existence”
JCAP04(200
Effects of scale-dependent non-Gaussianity on cosmological structures
LoVerde et al. (2008)
35. • Abundance of galaxy clusters
• Weak Lensing
• ...
• 21cm (?)
• μ-distorsions of the CMB spectrum (??)
Other probes
PNG affects the high-mass tail
of the cluster mass function
PNG affects also the nonlinear
evolution of the matter power
spectrum at small scales
All probes present significant
theoretical and numerical challenges!
36. Conclusions
• After the first PLANCK results the simplest model of inflation is alive
and kicking: no indication of any departure from a single-field, slow roll
inflation with canonical kinetic term from a Bunch-Davies vacuum
• PLACK will further improve its constraints by adding polarization
information
• Constraints on non-Gaussianity can, in some cases, severely reduce the
parameter space of many non-minimal models (without, however, ruling
them out)
• Future cosmological observations will focus on the large-scale structure:
the large volume available makes them, in principle, an even more powerful
probe of the initial conditions than the CMB
• However, the analysis of its several observables is challenging: we
have to deal with the nonlinear evolution of structures and the complex baryon
physics (to mention two among many problems ...!)
37. New Light in Cosmology
from the CMB
SCHOOL WORKSHOP
22 - 26 July 2013 29 July - 2 August 2013
Miramare, Trieste, Italy
TOPICS of the School:
• EARLY UNIVERSE
• CMB THEORY
• CMB EXPERIMENTS
• PLANCK PRODUCTS
• LENSING ISW
• BIG SCIENCE FROM SMALL SCALES
The purpose of the School is to provide the theoretical and computational tools to study the implications of
the recent results from CMB experiments. It is intended for graduate students, as well as more senior non-
expert researchers that are interested in these fields. The Workshop is devoted to the discussion of the
experimental CMB results in all their aspects, their relation with other probes and the future prospects.
PARTICIPATION
Scientists and students from all countries which are members of the United Nations, UNESCO or IAEA may
attend the School and Workshop. As it will be conducted in English, participants should have an adequate
working knowledge of this language. Although the main purpose of the Centre is to help research workers
from developing countries, through a programme of training activities within a framework of international
cooperation, students and post-doctoral scientists from advanced countries are also welcome to attend.
As a rule, travel and subsistence expenses of the participants should be borne by the home institution.
Every effort should be made by candidates to secure support for their fare (or at least half-fare). However,
limited funds are available for some participants who are nationals of, and working in, a developing country,
and who are not more than 45 years old. Such support is available only for those who attend the entire
activity. There is no registration fee to be paid.
HOW TO APPLY FOR PARTICIPATION:
The application forms can be accessed at the School Workshop website: http://agenda.ictp.it/smr.php?2474
Once in the website, comprehensive instructions will guide you step-by-step, on how to fill out and submit
the application forms.
SCHOOL WORKSHOP SECRETARIAT:
Telephone: +39 040 2240 363 - Telefax: +39 040 2240 7363 - E-mail: smr2474@ictp.it
ICTP Home Page: http://www.ictp.it/
IN COLLABORATION WITH
THE ITALIAN INSTITUTE FOR
NUCLEAR PHYSICS
ORGANIZERS:
C. Baccigalupi (SISSA)
P. Creminelli (ICTP)
R. Sheth (ICTP UPenn)
A. Zacchei (INAF - OATS)
LECTURERS:
C. Baccigalupi (SISSA)
A. Jaffe (Imperial College)
J. Lesgourgues (CERN EPFL)
A. Lewis (Sussex University)
L. Senatore (CERN Stanford)
R. Stompor (APC, Paris)
A. Zacchei (INAF - OATS)
SCIENTIFIC SECRETARY:
D. Lopez Nacir (ICTP)
DEADLINE
for requesting participation
15 April 2013
extended to
28 April 2013
January 2013
Deadline in 2 days!
38.
39. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
?
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
40. PNG in the last 10 years
?
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
non-primordial NG
41. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
COBE
(≪1σ)
WMAP1
(0.8 σ)
WMAP3
(0.7 σ)
WMAP7
(1.5 σ)
?
non-primordial NG
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
WMAP5
(1.7 σ)
Yadav Wandelt (2.8σ ?)
42. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
Inflation / Theory
non-primordial NG
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
COBE
(≪1σ)
WMAP1
(0.8 σ)
WMAP3
(0.7 σ)
WMAP7
(1.5 σ)
?
WMAP5
(1.7 σ)
Yadav Wandelt (2.8σ ?)
43. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
Inflation / Theory
non-primordial NG
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
CMB COBE
(≪1σ)
WMAP1
(0.8 σ)
WMAP3
(0.7 σ)
WMAP7
(1.5 σ)
?
WMAP5
(1.7 σ)
Yadav Wandelt (2.8σ ?)
44. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
Inflation / Theory
non-primordial NG
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
Large-Scale Structure
CMB COBE
(≪1σ)
WMAP1
(0.8 σ)
WMAP3
(0.7 σ)
WMAP7
(1.5 σ)
?
WMAP5
(1.7 σ)
Yadav Wandelt (2.8σ ?)
Dalal et al.
45. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
Inflation / Theory
non-primordial NG
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
Large-Scale Structure
CMB COBE
(≪1σ)
WMAP1
(0.8 σ)
WMAP3
(0.7 σ)
WMAP7
(1.5 σ)
?
WMAP5
(1.7 σ)
Yadav Wandelt (2.8σ ?)
Planck
fNL = 0?
Dalal et al.