The document discusses using an effective field theory (EFT) approach to test general relativity (GR) through gravitational wave detections. It outlines using the EFT method called non-relativistic GR (NRGR) to calculate post-Newtonian corrections and measure deviations from GR. NRGR translates corrections to binary inspiral into Feynman diagrams and provides tools to calculate radiation and conservative dynamics. Measuring the quadrupole formula through detections could probe the non-linearities and vertices of GR.
The document discusses probing CP violation in supersymmetric stop decays at the LHC. It proposes using triple product asymmetries, which are CP-odd observables, to measure CP-violating phases like φAt and φμ. These asymmetries could allow detection of CP violation in stop decays via spin correlations with the second lightest neutralino at the LHC, providing an alternative to constraints from electric dipole moments. Large asymmetries and sensitivity to the CP phases are possible, and a detailed experimental analysis is motivated.
The document describes several physics experiments and concepts:
1. Davisson and Germer experiment which demonstrated the wave nature of electrons using electron diffraction from a nickel crystal. The experiment found maximum scattering intensity at specific angles that matched Bragg's law.
2. Frequency modulation in radio which varies the frequency of the carrier wave based on the audio frequency signal. It provides advantages over amplitude modulation like resistance to noise.
3. Gauss's law and how it can be used to derive Coulomb's law of electrostatics.
4. The working principle of a Van de Graaff generator which uses a moving belt to build up high voltages on a large spherical conductor.
5. The design and working of
The document summarizes a workshop on structure borne noise, vibration, and harshness (NVH) basics. It includes an outline of workshop topics such as fundamentals of NVH, load conditions, and low frequency basics. The workshop covers key concepts like the relationship between time and frequency domains, vibration isolation principles, and common NVH attenuation methods like reducing input forces, providing isolation, and using dynamic absorbers. Examples are provided to illustrate NVH modeling and the effect of isolation on vibration response. The goal is to reveal the fundamental secrets of structure borne NVH performance.
Video Copy Detection Using Inclined Video Tomography and Bag-of-Visual-WordsWesley De Neve
This document proposes a new approach to video copy detection using inclined video tomography and bag-of-visual-words. It extracts inclined tomography images from video clips at different angles based on motion, then characterizes the images using bag-of-visual-words. An experiment applies transformations to video clips and measures the precision of detecting the original clips using histograms of visual word weights between clips. Results show the approach can effectively detect transformed video copies while exploiting both spatial and temporal information.
The Radon-Nikody ́m Theorem for vector measures and factorization of operator...esasancpe
This document presents notation and concepts related to Banach function spaces, including:
- Banach function spaces (B.f.s.) defined over a finite measure space
- Multiplication operators between B.f.s. and their associated multiplier spaces
- Product spaces of two B.f.s. and properties like order continuity
It also states a theorem regarding when the product space of two B.f.s. is order continuous.
1. The document discusses a lecture on baryon acoustic oscillations (BAO) and dark energy given by Bruce Bassett.
2. BAO are density fluctuations in the early universe that were imprinted by sound waves propagating in the plasma of photons and baryons before recombination. These fluctuations provide a "standard ruler" that can be used to measure cosmic distances and expansion.
3. Bassett discusses the origin and detection of BAO, optimal survey design for BAO measurements, and complications including non-linear evolution and use of photometric rather than spectroscopic surveys. He emphasizes BAO as a low-redshift cosmic distance measure based on linear physics.
The document summarizes Bruce Bassett's presentation on baryon acoustic oscillations (BAO) and dark energy. It discusses:
1) How BAO originated from acoustic oscillations in the early universe plasma of photons and baryons, leaving an imprint in the clustering of galaxies today at a characteristic scale of 150 Mpc.
2) How BAO can be used as a "standard ruler" to measure cosmic distances and expansion history by detecting this characteristic scale in galaxy clustering statistics like the 2-point correlation function and power spectrum.
3) Some of the challenges in detecting the BAO signal, which requires large galaxy surveys to overcome shot noise and cosmic variance, and how different
The document is an excerpt from someone's journal describing themselves as an "angel of justice" who takes the law into their own hands. They describe waiting 18 years to kill a man who they feel deserves to die for an unknown crime and detailing the act of killing him with stabs. They also mention having a son and needing to flee after he hears the murder, hoping to one day return for him, as the police will investigate the killing.
The document discusses probing CP violation in supersymmetric stop decays at the LHC. It proposes using triple product asymmetries, which are CP-odd observables, to measure CP-violating phases like φAt and φμ. These asymmetries could allow detection of CP violation in stop decays via spin correlations with the second lightest neutralino at the LHC, providing an alternative to constraints from electric dipole moments. Large asymmetries and sensitivity to the CP phases are possible, and a detailed experimental analysis is motivated.
The document describes several physics experiments and concepts:
1. Davisson and Germer experiment which demonstrated the wave nature of electrons using electron diffraction from a nickel crystal. The experiment found maximum scattering intensity at specific angles that matched Bragg's law.
2. Frequency modulation in radio which varies the frequency of the carrier wave based on the audio frequency signal. It provides advantages over amplitude modulation like resistance to noise.
3. Gauss's law and how it can be used to derive Coulomb's law of electrostatics.
4. The working principle of a Van de Graaff generator which uses a moving belt to build up high voltages on a large spherical conductor.
5. The design and working of
The document summarizes a workshop on structure borne noise, vibration, and harshness (NVH) basics. It includes an outline of workshop topics such as fundamentals of NVH, load conditions, and low frequency basics. The workshop covers key concepts like the relationship between time and frequency domains, vibration isolation principles, and common NVH attenuation methods like reducing input forces, providing isolation, and using dynamic absorbers. Examples are provided to illustrate NVH modeling and the effect of isolation on vibration response. The goal is to reveal the fundamental secrets of structure borne NVH performance.
Video Copy Detection Using Inclined Video Tomography and Bag-of-Visual-WordsWesley De Neve
This document proposes a new approach to video copy detection using inclined video tomography and bag-of-visual-words. It extracts inclined tomography images from video clips at different angles based on motion, then characterizes the images using bag-of-visual-words. An experiment applies transformations to video clips and measures the precision of detecting the original clips using histograms of visual word weights between clips. Results show the approach can effectively detect transformed video copies while exploiting both spatial and temporal information.
The Radon-Nikody ́m Theorem for vector measures and factorization of operator...esasancpe
This document presents notation and concepts related to Banach function spaces, including:
- Banach function spaces (B.f.s.) defined over a finite measure space
- Multiplication operators between B.f.s. and their associated multiplier spaces
- Product spaces of two B.f.s. and properties like order continuity
It also states a theorem regarding when the product space of two B.f.s. is order continuous.
1. The document discusses a lecture on baryon acoustic oscillations (BAO) and dark energy given by Bruce Bassett.
2. BAO are density fluctuations in the early universe that were imprinted by sound waves propagating in the plasma of photons and baryons before recombination. These fluctuations provide a "standard ruler" that can be used to measure cosmic distances and expansion.
3. Bassett discusses the origin and detection of BAO, optimal survey design for BAO measurements, and complications including non-linear evolution and use of photometric rather than spectroscopic surveys. He emphasizes BAO as a low-redshift cosmic distance measure based on linear physics.
The document summarizes Bruce Bassett's presentation on baryon acoustic oscillations (BAO) and dark energy. It discusses:
1) How BAO originated from acoustic oscillations in the early universe plasma of photons and baryons, leaving an imprint in the clustering of galaxies today at a characteristic scale of 150 Mpc.
2) How BAO can be used as a "standard ruler" to measure cosmic distances and expansion history by detecting this characteristic scale in galaxy clustering statistics like the 2-point correlation function and power spectrum.
3) Some of the challenges in detecting the BAO signal, which requires large galaxy surveys to overcome shot noise and cosmic variance, and how different
The document is an excerpt from someone's journal describing themselves as an "angel of justice" who takes the law into their own hands. They describe waiting 18 years to kill a man who they feel deserves to die for an unknown crime and detailing the act of killing him with stabs. They also mention having a son and needing to flee after he hears the murder, hoping to one day return for him, as the police will investigate the killing.
Tara runs away from her abusive adoptive father in an attempt to find freedom and happiness. She manages to escape from her apartment and takes a series of buses to the small town of Riverblossom Hills. However, upon arriving, she realizes she left her suitcase on the last bus. An unscrupulous man named Snidely Whiplash overhears her situation and tricks her into an unspecified agreement, hypnotizing her and coercing her to verbally agree to undisclosed terms in exchange for promises of a home, family, money and love.
The document introduces the Folie á Deux legacy and the story of Generation 1. It summarizes that Phoenix and Timothy had a loving family together until one night Timothy turned into a werewolf and killed Phoenix in a rage. Their children Sydney, Alicia, Kaidan and India then escaped in a stolen car and Timothy later committed suicide with poison in the garden. The story is passed on to Jess to continue playing as Sydney and the Folie á Deux legacy.
Research is an intellectual activity aimed at discovering and advancing human knowledge. It requires breaking new ground, which is always hard. Research may not be for everyone as it requires flexibility and a willingness to move locations for work. It also takes time to establish a career. However, research allows flexibility in choosing topics and approaches. Being a researcher involves setbacks but also opportunities to address deep problems. Publishing research requires new ideas, data analysis, theoretical studies, or presenting new tools. Choosing a supervisor and topic that match one's interests and skills is important for success. Developing skills in areas like time management, collaboration, writing and presentation are also important for a career in research.
The document discusses the "cosmological coincidence" which refers to the fact that the current epoch is favorable for the emergence of life. It presents the view that we should not be surprised to find ourselves in a time when the universe is consistent with life since we would not exist otherwise. Several proposed solutions to address the coincidence are mentioned, including the idea that carbon is common, planets form at late times, or the multiverse theory where other universes exist with different physical laws and constants.
Matt Jarvis - Recent results from the Herschel-ATLASCosmoAIMS Bassett
The recent results from the Herschel ATLAS survey can be summarized as follows:
1) The Herschel ATLAS survey has detected over 100,000 far-infrared galaxies out to redshift z=3 using Herschel's PACS and SPIRE instruments.
2) Studies of the far-infrared properties and clustering of these galaxies are providing insights into the evolution of dust in galaxies and galaxy formation over cosmic time.
3) The large area of the Herschel ATLAS survey has also led to the detection of strongly lensed high-redshift galaxies and fluctuations in the far-infrared background.
Yabebal Fantaye - Estimating Tensor to Scalar RatioCosmoAIMS Bassett
This document discusses estimating the tensor-to-scalar ratio from cosmic microwave background polarization measurements. It provides background on CMB polarization, including how density perturbations and gravitational waves create E-mode and B-mode polarization patterns. Extracting the CMB polarization signal requires cleaning foreground contamination from galactic synchrotron and dust emission. Component separation methods aim to separate the CMB, synchrotron, and dust signals using multi-frequency data. Estimating the tensor-to-scalar ratio also requires accounting for the covariance from instrument noise and residual foregrounds in power spectrum estimation and parameter constraints.
The document discusses using machine learning techniques to classify astronomical objects from large surveys. It notes that surveys are producing huge amounts of data that conventional methods cannot fully process. Machine learning can be used to help classify objects and sort candidates. Specifically, the document discusses using machine learning on photometric data from the Sloan Digital Sky Survey (SDSS) to identify low-redshift quasars. It notes challenges including the large size and dimensionality of the data, and proposes using a boosted ensemble method to learn weights for different regions of feature space rather than trying to estimate probabilities. This would help classify objects from the SDSS into categories like quasars, stars or galaxies.
SN Ia Rate in Intermediate-Redshift Galaxy Clusters - Eli KasaiCosmoAIMS Bassett
This document outlines Eli Kasai's thesis on measuring the rate of Type Ia supernovae (SN Ia) in intermediate-redshift galaxy clusters. It discusses using image subtraction algorithms like IRAF and ISIS to detect transient objects like SN Ia in images of galaxy clusters taken over multiple epochs. It compares the IRAF algorithm which takes around a week to process images to the automated ISIS algorithm which can do it in 3-4 hours. The goal is to better understand progenitor models of SN Ia and improve cosmological parameters.
Modelling the Atomic and Molecular Gas in Galaxies and Comparisons wih GASS a...CosmoAIMS Bassett
This document discusses modeling the atomic and molecular gas content of galaxies and comparing models to observational results from surveys like GASS and COLD GASS. The modeling involves simulations of galaxy formation that track the infall and cooling of gas. Comparisons show the models match observed gas mass functions but gas profiles in simulations are too flat compared to data. Improving dissipation of supernova energy in dense inner disks improves fits. Non-detected gas fractions in data depend on structure, not just mass. This suggests bulge/black hole growth, not just mass, quenches star formation. Photometric predictors of atomic gas are also explored.
Cross Matching EUCLID and SKA using the Likelihood RatioCosmoAIMS Bassett
1) The document discusses using a likelihood ratio technique to identify counterparts between low-resolution radio data from surveys like SKA and optical/infrared data from surveys like Euclid.
2) The likelihood ratio technique calculates probabilities that potential counterparts are true matches versus random alignments based on positional offsets and magnitude distributions.
3) Applying the technique to simulated lower-resolution radio data shows a 3-5% loss in identified counterparts compared to high-resolution data, with the worst effects for faint radio sources. However, the vast majority of identified counterparts remain the same.
The 21cm line from neutral hydrogen can be used to study cosmology during the first billion years of the universe. This includes the Dark Ages when no structures formed, the Cosmic Dawn when the first luminous objects formed, and the Epoch of Reionization when these objects reionized the intergalactic medium. Current and future 21cm experiments like LOFAR, MWA, PAPER, and HERA aim to detect the signal from these eras but face challenges in calibrating the instruments and subtracting bright foreground sources. Some progress has been made in placing upper limits on the signal and constraining the heating of the intergalactic medium by X-rays, but a clear detection of the signal is still needed
Binary pulsars provide an excellent tool to test theories of gravity. The document describes several binary pulsar systems and how measurements of their orbital parameters over time have allowed for high-precision tests of general relativity in strong gravitational fields. Specifically, the double pulsar system PSR J0737-3039A/B has enabled measurements that agree with general relativity predictions to within 0.05% precision by measuring parameters like periastron advance and gravitational redshift effects.
This document summarizes research on the impact of allowing for general isocurvature perturbations and cosmic curvature in analyses of baryon acoustic oscillations (BAO) as a probe of dark energy. The key points are:
1) Accounting for general isocurvature modes could bias dark energy parameter estimates from stage III-IV surveys by over 7 sigma, incorrectly measuring w0 and up to 23 sigma for wa.
2) Including isocurvature modes degrades the dark energy figure of merit from BAO data by at least 50% for experiments like BOSS.
3) BAO provide stronger constraints on the primordial perturbations than CMB alone. Allowing dynamical dark energy and curvature adds little
This document discusses the effective field theory of multi-field inflation based on Weinberg's approach. It constructs the most general Lagrangian for the background and perturbation terms up to fourth order. For the multi-field case, the Lagrangian contains terms for both the adiabatic and entropy perturbations. The validity of the effective field theory constrains the possible amplitude of non-Gaussianities produced during inflation. This approach differs from previous work by defining perturbations before distinguishing adiabatic and entropy modes.
This document discusses non-Gaussianities in the cosmic microwave background from multifield inflation models. It summarizes that generating a large local form of non-Gaussianity (fNL) requires super-horizon evolution of the curvature perturbation after inflation, which can be achieved if the fields have isocurvature perturbations. However, multifield models are incomplete if they do not track the perturbations all the way to the final adiabatic post-inflationary state. The document outlines developing a toy model that captures the key physics of when adiabaticity is achieved to better understand the generation and freezing of fNL.
The document presents a study using simulated type Ia supernova data to investigate how peculiar velocities affect constraints on cosmological parameters from supernova observations. The study generates a simulated supernova dataset that includes peculiar velocity information. It then constructs Hubble diagrams using true and observed redshifts from the simulations. The resulting parameter estimates are compared, finding the peculiar velocities can induce shifts in the estimated values of Ωm and H0 of approximately 1 sigma.
The document provides an overview of CMB experiments, including:
1) It describes the natural units used to measure CMB temperature and polarization maps, and how the power spectrum is derived from harmonic coefficients of the maps.
2) It shows the predicted scalar power spectrum, noting the first acoustic peak at l≈220 and subsequent Doppler peaks and troughs.
3) It discusses how instrument noise is characterized and how the likelihood function relates observed and theoretical power spectra.
4) It briefly describes how the CMB is predicted to be mildly polarized and how polarization is represented, as well as technologies used to detect CMB fluctuations like microwave horns.
This document discusses machine learning concepts including supervised vs. unsupervised learning, clustering algorithms, and specific clustering methods like k-means and k-nearest neighbors. It provides examples of how clustering can be used for applications such as market segmentation and astronomical data analysis. Key clustering algorithms covered are hierarchy methods, partitioning methods, k-means which groups data by assigning objects to the closest cluster center, and k-nearest neighbors which classifies new data based on its closest training examples.
Tara runs away from her abusive adoptive father in an attempt to find freedom and happiness. She manages to escape from her apartment and takes a series of buses to the small town of Riverblossom Hills. However, upon arriving, she realizes she left her suitcase on the last bus. An unscrupulous man named Snidely Whiplash overhears her situation and tricks her into an unspecified agreement, hypnotizing her and coercing her to verbally agree to undisclosed terms in exchange for promises of a home, family, money and love.
The document introduces the Folie á Deux legacy and the story of Generation 1. It summarizes that Phoenix and Timothy had a loving family together until one night Timothy turned into a werewolf and killed Phoenix in a rage. Their children Sydney, Alicia, Kaidan and India then escaped in a stolen car and Timothy later committed suicide with poison in the garden. The story is passed on to Jess to continue playing as Sydney and the Folie á Deux legacy.
Research is an intellectual activity aimed at discovering and advancing human knowledge. It requires breaking new ground, which is always hard. Research may not be for everyone as it requires flexibility and a willingness to move locations for work. It also takes time to establish a career. However, research allows flexibility in choosing topics and approaches. Being a researcher involves setbacks but also opportunities to address deep problems. Publishing research requires new ideas, data analysis, theoretical studies, or presenting new tools. Choosing a supervisor and topic that match one's interests and skills is important for success. Developing skills in areas like time management, collaboration, writing and presentation are also important for a career in research.
The document discusses the "cosmological coincidence" which refers to the fact that the current epoch is favorable for the emergence of life. It presents the view that we should not be surprised to find ourselves in a time when the universe is consistent with life since we would not exist otherwise. Several proposed solutions to address the coincidence are mentioned, including the idea that carbon is common, planets form at late times, or the multiverse theory where other universes exist with different physical laws and constants.
Matt Jarvis - Recent results from the Herschel-ATLASCosmoAIMS Bassett
The recent results from the Herschel ATLAS survey can be summarized as follows:
1) The Herschel ATLAS survey has detected over 100,000 far-infrared galaxies out to redshift z=3 using Herschel's PACS and SPIRE instruments.
2) Studies of the far-infrared properties and clustering of these galaxies are providing insights into the evolution of dust in galaxies and galaxy formation over cosmic time.
3) The large area of the Herschel ATLAS survey has also led to the detection of strongly lensed high-redshift galaxies and fluctuations in the far-infrared background.
Yabebal Fantaye - Estimating Tensor to Scalar RatioCosmoAIMS Bassett
This document discusses estimating the tensor-to-scalar ratio from cosmic microwave background polarization measurements. It provides background on CMB polarization, including how density perturbations and gravitational waves create E-mode and B-mode polarization patterns. Extracting the CMB polarization signal requires cleaning foreground contamination from galactic synchrotron and dust emission. Component separation methods aim to separate the CMB, synchrotron, and dust signals using multi-frequency data. Estimating the tensor-to-scalar ratio also requires accounting for the covariance from instrument noise and residual foregrounds in power spectrum estimation and parameter constraints.
The document discusses using machine learning techniques to classify astronomical objects from large surveys. It notes that surveys are producing huge amounts of data that conventional methods cannot fully process. Machine learning can be used to help classify objects and sort candidates. Specifically, the document discusses using machine learning on photometric data from the Sloan Digital Sky Survey (SDSS) to identify low-redshift quasars. It notes challenges including the large size and dimensionality of the data, and proposes using a boosted ensemble method to learn weights for different regions of feature space rather than trying to estimate probabilities. This would help classify objects from the SDSS into categories like quasars, stars or galaxies.
SN Ia Rate in Intermediate-Redshift Galaxy Clusters - Eli KasaiCosmoAIMS Bassett
This document outlines Eli Kasai's thesis on measuring the rate of Type Ia supernovae (SN Ia) in intermediate-redshift galaxy clusters. It discusses using image subtraction algorithms like IRAF and ISIS to detect transient objects like SN Ia in images of galaxy clusters taken over multiple epochs. It compares the IRAF algorithm which takes around a week to process images to the automated ISIS algorithm which can do it in 3-4 hours. The goal is to better understand progenitor models of SN Ia and improve cosmological parameters.
Modelling the Atomic and Molecular Gas in Galaxies and Comparisons wih GASS a...CosmoAIMS Bassett
This document discusses modeling the atomic and molecular gas content of galaxies and comparing models to observational results from surveys like GASS and COLD GASS. The modeling involves simulations of galaxy formation that track the infall and cooling of gas. Comparisons show the models match observed gas mass functions but gas profiles in simulations are too flat compared to data. Improving dissipation of supernova energy in dense inner disks improves fits. Non-detected gas fractions in data depend on structure, not just mass. This suggests bulge/black hole growth, not just mass, quenches star formation. Photometric predictors of atomic gas are also explored.
Cross Matching EUCLID and SKA using the Likelihood RatioCosmoAIMS Bassett
1) The document discusses using a likelihood ratio technique to identify counterparts between low-resolution radio data from surveys like SKA and optical/infrared data from surveys like Euclid.
2) The likelihood ratio technique calculates probabilities that potential counterparts are true matches versus random alignments based on positional offsets and magnitude distributions.
3) Applying the technique to simulated lower-resolution radio data shows a 3-5% loss in identified counterparts compared to high-resolution data, with the worst effects for faint radio sources. However, the vast majority of identified counterparts remain the same.
The 21cm line from neutral hydrogen can be used to study cosmology during the first billion years of the universe. This includes the Dark Ages when no structures formed, the Cosmic Dawn when the first luminous objects formed, and the Epoch of Reionization when these objects reionized the intergalactic medium. Current and future 21cm experiments like LOFAR, MWA, PAPER, and HERA aim to detect the signal from these eras but face challenges in calibrating the instruments and subtracting bright foreground sources. Some progress has been made in placing upper limits on the signal and constraining the heating of the intergalactic medium by X-rays, but a clear detection of the signal is still needed
Binary pulsars provide an excellent tool to test theories of gravity. The document describes several binary pulsar systems and how measurements of their orbital parameters over time have allowed for high-precision tests of general relativity in strong gravitational fields. Specifically, the double pulsar system PSR J0737-3039A/B has enabled measurements that agree with general relativity predictions to within 0.05% precision by measuring parameters like periastron advance and gravitational redshift effects.
This document summarizes research on the impact of allowing for general isocurvature perturbations and cosmic curvature in analyses of baryon acoustic oscillations (BAO) as a probe of dark energy. The key points are:
1) Accounting for general isocurvature modes could bias dark energy parameter estimates from stage III-IV surveys by over 7 sigma, incorrectly measuring w0 and up to 23 sigma for wa.
2) Including isocurvature modes degrades the dark energy figure of merit from BAO data by at least 50% for experiments like BOSS.
3) BAO provide stronger constraints on the primordial perturbations than CMB alone. Allowing dynamical dark energy and curvature adds little
This document discusses the effective field theory of multi-field inflation based on Weinberg's approach. It constructs the most general Lagrangian for the background and perturbation terms up to fourth order. For the multi-field case, the Lagrangian contains terms for both the adiabatic and entropy perturbations. The validity of the effective field theory constrains the possible amplitude of non-Gaussianities produced during inflation. This approach differs from previous work by defining perturbations before distinguishing adiabatic and entropy modes.
This document discusses non-Gaussianities in the cosmic microwave background from multifield inflation models. It summarizes that generating a large local form of non-Gaussianity (fNL) requires super-horizon evolution of the curvature perturbation after inflation, which can be achieved if the fields have isocurvature perturbations. However, multifield models are incomplete if they do not track the perturbations all the way to the final adiabatic post-inflationary state. The document outlines developing a toy model that captures the key physics of when adiabaticity is achieved to better understand the generation and freezing of fNL.
The document presents a study using simulated type Ia supernova data to investigate how peculiar velocities affect constraints on cosmological parameters from supernova observations. The study generates a simulated supernova dataset that includes peculiar velocity information. It then constructs Hubble diagrams using true and observed redshifts from the simulations. The resulting parameter estimates are compared, finding the peculiar velocities can induce shifts in the estimated values of Ωm and H0 of approximately 1 sigma.
The document provides an overview of CMB experiments, including:
1) It describes the natural units used to measure CMB temperature and polarization maps, and how the power spectrum is derived from harmonic coefficients of the maps.
2) It shows the predicted scalar power spectrum, noting the first acoustic peak at l≈220 and subsequent Doppler peaks and troughs.
3) It discusses how instrument noise is characterized and how the likelihood function relates observed and theoretical power spectra.
4) It briefly describes how the CMB is predicted to be mildly polarized and how polarization is represented, as well as technologies used to detect CMB fluctuations like microwave horns.
This document discusses machine learning concepts including supervised vs. unsupervised learning, clustering algorithms, and specific clustering methods like k-means and k-nearest neighbors. It provides examples of how clustering can be used for applications such as market segmentation and astronomical data analysis. Key clustering algorithms covered are hierarchy methods, partitioning methods, k-means which groups data by assigning objects to the closest cluster center, and k-nearest neighbors which classifies new data based on its closest training examples.
- The document discusses methods for characterizing dark energy and modified gravity models in a model-independent way using cosmological observations.
- Due to the "dark degeneracy" between dark matter and dark energy, it is not possible to separately measure the properties of dark matter and dark energy without assuming a specific model class.
- Observables like the Hubble parameter H(z) and gravitational potentials can be reconstructed from the data, but this does not break the degeneracy between dark matter and dark energy contributions.
- The scale-dependence of quantities like the gravitational potentials and growth rate can be used to test and constrain broad classes of dark energy and modified gravity models in a more model-independent way.
Seminar by Prof Bruce Bassett at IAP, Paris, October 2013CosmoAIMS Bassett
This document discusses the rise of machine learning and artificial intelligence in astronomy due to a massive increase in data from upcoming surveys. It will produce around an exabyte of data per day, far more than has been produced throughout human history. This raises issues around preparing students, and how science may be done. The document discusses using machine learning for tasks like supernova identification and classification. It also discusses challenges like ensuring machine learning results are trustworthy, and whether this can truly replace human genius. It explores the idea of a universal language for scientific theories that could be searched algorithmically.
The document discusses the cosmic dawn and reionization period in the early universe. It describes the evolution from the dark ages after recombination to the epoch of reionization around z=6-20. Key aspects discussed include understanding the sources and sinks of ionizing photons that drove reionization, and challenges in modeling this period due to the large parameter space and scales involved, from single stars to the entire universe. Seminumerical simulations are presented as an efficient method to model reionization and predict 21cm signals.
A short introduction to massive gravity... or ... Can one give a mass to the ...CosmoAIMS Bassett
1. The document discusses massive gravity and proposes that giving the graviton a small mass could potentially explain dark matter and dark energy without needing to introduce those concepts.
2. It reviews several models of massive gravity, including the Dvali-Gabadadze-Porrati model, which produces cosmic acceleration similar to dark energy. Kaluza-Klein theory is also discussed as producing massive gravitons.
3. Nonlinear extensions of the Pauli-Fierz theory are examined, finding solutions only with singularities. The "Goldstone" description of massive gravity is introduced as a way to better understand nonlinear effects like the Vainshtein mechanism.
This document summarizes recent research on how the sizes and densities of galaxies have changed over time. Studies have found that galaxies at high redshift had smaller sizes than present-day galaxies of the same mass, often by a factor of 2-3 within 1 kpc and over 100 times within the effective radius. Various mechanisms are discussed for how galaxies could have grown, including minor mergers which could increase size more than mass over time. The document also examines constraints on the amount of growth massive galaxies could have experienced through mergers between redshifts of 0.8 to 0.1 based on the luminosity and stellar mass functions remaining largely unchanged over this period.
Cluster abundances and clustering Can theory step up to precision cosmology?CosmoAIMS Bassett
This document discusses improvements to the Press-Schechter theory for modeling the abundances and clustering of dark matter halos. It proposes that modeling halo collapse as requiring the density to "step up" above a critical density threshold at progressively larger spatial scales provides a better approximation than assuming fully correlated or uncorrelated densities. This "stepping up" approach requires only 2-point statistics and can be applied to non-Gaussian fields. The document also suggests that modeling the distribution of density slopes at peak positions provides a way to match halo counts through an Excursion Set Peaks model.
This document discusses gravitational lensing and some of the challenges involved in measuring it. Gravitational lensing causes the apparent deflection of light from distant background sources as it passes massive foreground objects. Precise measurements of lensing effects can provide information about dark matter distributions and the geometry and growth of the universe. However, there are three main problems: accurately measuring galaxy shapes used to detect lensing distortions, determining reliable photometric redshifts for galaxies, and accounting for intrinsic alignments of galaxy orientations unrelated to lensing.
Testing cosmology with galaxy clusters, the CMB and galaxy clusteringCosmoAIMS Bassett
This document summarizes a presentation on testing cosmology using galaxy clusters, the cosmic microwave background, and galaxy clustering. It discusses combining measurements of cosmic growth and expansion from these sources to constrain departures from general relativity. Models are presented for linear, time-dependent departures from GR. Constraints on parameters like the growth index γ are shown from combinations of clusters, CMB, and galaxy data. Tightening constraints are achieved by adding baryon acoustic oscillation, supernova, and Hubble constant data. The document also briefly discusses using cluster counts to constrain primordial non-Gaussianity.
This document discusses galaxy formation and evolution from cosmological simulations and models. It summarizes that galaxy formation is driven by the hierarchical growth of dark matter halos, gas accretion via cold filamentary streams or hot spherical halos, and feedback regulating star formation. Galaxy properties like star formation rates and metallicities are set by the balance between gas inflow and outflow.
Spit, Duct Tape, Baling Wire & Oral Tradition: Dealing With Radio DataCosmoAIMS Bassett
The document discusses the process of creating radio interferometers and summarizing data from them. It begins with an overview of how a normal reflector telescope can be broken up and transformed into an interferometer by replacing the optical path with electronics and correlating signals between antenna elements. It then discusses some of the challenges in summarizing interferometer data, including missing information due to an incomplete coverage of the uv-plane, measurement errors that distort the signals, and direction-dependent effects that vary with time, antenna, and direction. The document introduces the concept of the Radio Interferometer Measurement Equation (RIME) to formally describe these direction-dependent distortions.
The document summarizes the MeerKAT radio telescope project in South Africa, including:
- MeerKAT will be the largest radio telescope in the southern hemisphere and one of the largest in the world, establishing a legacy for Africa. It is an SKA precursor project.
- The specifications for MeerKAT including the number of antennas, maximum baseline, bandwidth, frequency range, and survey plans.
- MeerKAT will initially consist of 64 antennas in 2016, expanding over time. It aims to carry out a number of surveys for HI, pulsars, galaxies, and fast/slow transients.
- Opportunities are outlined for students and faculty to get involved in radio astronomy research
This document provides guidance on reducing interferometric radio astronomy data from the Karoo Array Telescope (KAT-7) using the Common Astronomy Software Applications (CASA). It describes the multi-step process of calibration and imaging required to produce an image from the visibility measurements made by an interferometer. The key steps involve: 1) converting the raw data from HDF5 format to a measurement set, 2) loading and inspecting the data, 3) flagging bad or corrupted data, 4) solving for the complex gain calibration terms using calibrator sources, 5) splitting the data for source and calibrator, 6) deconvolving the dirty image using CLEAN to account for incomplete uv-coverage. Trouble
From Darkness, Light: Computing Cosmological ReionizationCosmoAIMS Bassett
1) Reionization occurred between redshifts of 10-6, beginning around 10 billion years ago and ending around 1 billion years ago.
2) Observations of the CMB and galaxies at z>6 provide constraints but questions remain about the sources and topology of reionization.
3) Cosmological simulations of reionization must model structure formation, radiation transport, and non-equilibrium chemistry and physics to help address open questions.
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With Metta,
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إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
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تتميز هذهِ الملزمة بعِدة مُميزات :
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2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
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واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
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SWOT analysis in the project Keeping the Memory @live.pptx
Hillary Sanctuary's Cosmology Seminar
1. Effective Field Theory
Approach to Testing GR
AIMS, Cape Town
September 1st 2010
Hillary Sanctuary
Friday, September 17, 2010
2. Outline
I. Brief introduction to GWs
II. Motivation : probe non-linearities of GR
III. Tools : Effective Field Theory Method (NRGR)
IV. Measuring deviations from GR. Physics beyond GR?
Friday, September 17, 2010
3. Results
• Measurement of radiation loss from the Hulse-
Taylor Binary provides an important confirmation
of the gauge structure of GR to 0.1%.
• Careful: provides experimental bounds unknown
physics IF General Relativity is the correct low-
energy theory of gravity.
Friday, September 17, 2010
4. I. Introduction to GW
• Gravitational waves are oscillations of the
“fabric” of spacetime.
• To see this (weak field limit) of Einstein’s eqns:
gµν ηµν hµν
|hµν |
Friday, September 17, 2010
6. Binary Pulsar : important test
A pulsar is a highly magnetized, rotating neutron star that emits EM radiation.
A binary pulsar is a pulsar + companion.
Friday, September 17, 2010
7. Hulse-Taylor Binary (1974)
The pulsar rotates on its axis17 times per second, pulse period is 59ms.
The orbital period is 7.75 hours.
Separation at periastron: 1,000,000 km.
Inspiral for 300,000,000 years.
Gravitational waves?
Friday, September 17, 2010
8. Inferred detection.
Orbital decay due to energy loss via gravitational radiation.
The data points indicate the observed
change in the epoch of periastron with
date while the parabola illustrates the
theoretically expected change in epoch
according to GR. astro-ph/0407149
Friday, September 17, 2010
9. Quest for direct detection
Network of GW detectors
(LIGO,Virgo, LISA,etc)
Friday, September 17, 2010
10. A closer look
Animation: h ∼ 0.5
f ∼ 2 seconds
BH coalescence:
(10M⊙ , r = 10RS , R = 100 Mpc)
h ∼ 10−21
f ∼ 100 seconds−1
Friday, September 17, 2010
11. Estimates at interferometers
Physical effect of a passing GW, perturb relative positions of freely-falling masses:
δL
∼h
L
h L
δL ∼ 10 −16
cm
10 −21 km
Bohr radius (atom): a0 ∼ 5 × 10−9 cm
Nucleus: 1 f m = 10−13 cm
Need to measure miniscule perturbations.
Friday, September 17, 2010
12. Sources Sensitivity Curves
SB
SB
h
th
ed
SB
rs
nc
h
Fi
Best candidates for
ed
ha
nc
En
25BH/25BH
va
10-20 Inspiral @ 150Mpc
Rin
earth-based detectors:
Ad
Collision gd
SN hang
own
NS/NS @ up @ 10
30Mpc o 0km, 15M
r 10BH/1
BH and NS
0BH @ 1 pc
hc = h!n 50Mpc
gup c
han 15Mp
10-21
@2
SN km ,
0
coalescences.
Rin
Inspiral
gdo
Collision
NS/NS @
300Mpc
wn
or 10BH
/10BH @
150
30B 0Mpc
SN Boiling @ z H/30B
10-22 at 20 kpc =1 H
10 100 1000 10000
frequency, Hz
igure 3: LIGO’s projected broad-band noise sensitivity to bursts hSB (Refs. [12, 15]) compared
ith the characteristic amplitudes hc of the waves from several hypothesized sources. The signal
√
o noise ratios are 2 higher than in Ref. [12] because of a factor 2 error in Eq. (29) of Ref. [11].
Friday, September 17, 2010
13. Example: NS-NS coalescence 3.1 Inspiral of binary stars 137
!
Fig. 3.2 The time evolution of the GW amplitude in the inspiral phase of a binary
system.
1.45M⊙
Using the explicit expression (3.16) we find (recall that ∂/∂τ = −∂/∂t)
Φ(τ ) = −2 45 kmτ
5GM
c3
c
−5/8
5/8
+ Φ0 , (3.29)
where Φ0 = Φ(τ = 0) is an arXiv:0804.0594
integration constant, equal to the value of Φ
at coalescence. Since both fgw , given in eq. (3.16) and Φ in eq. (3.29)
depend only on the combination τ , the GW amplitude can be expressed
directly in terms of the time t of the observer, and the time of coalescence
of the observer, tcoal ,
5/4 1/4
1 GMc 5 1 + cos2 ι
h+ (t) = cos [Φ(τ )] ,
r c2 cτ 2
5/4 1/4
1 GMc 5
h× (t) = cos ι sin [Φ(τ )] , (3.30)
r c2 cτ
where
Friday, September 17, 2010
14. Example: NS-NS coalescence 3.1 Inspiral of binary stars 137
!
Fig. 3.2 The time evolution of the GW amplitude in the inspiral phase of a binary
system.
1.45M⊙
Using the explicit expression (3.16) we find (recall that ∂/∂τ = −∂/∂t)
Φ(τ ) = −2 45 kmτ
5GM
c3
c
−5/8
5/8
+ Φ0 , (3.29)
where Φ0 = Φ(τ = 0) is an arXiv:0804.0594
integration constant, equal to the value of Φ
at coalescence. Since both fgw , given in eq. (3.16) and Φ in eq. (3.29)
depend only on the combination τ , the GW amplitude can be expressed
directly in terms of the time t of the observer, and the time of coalescence
of the observer, tcoal ,
5/4 1/4
1 GMc 5 1 + cos2 ι
h+ (t) = cos [Φ(τ )] ,
r c2 cτ 2
5/4 1/4
1 GMc 5
h× (t) = cos ι sin [Φ(τ )] , (3.30)
r c2 cτ
where
Friday, September 17, 2010
15. II. Motivation
• GR is non-linear
• Two labs where non-linearities are at work
(binary pulsars, coalescences)
• Non-linearities (non-abelian vertices):
• Can we measure these vertices? YES
(Tevatron, LEP for SM, deviations from GR?)
Friday, September 17, 2010
16. Post-Newtonian Expansion
• What is it? Post-Newtonian terms in GR are
corrections to Newtonian Gravity in powers of
v/c 1 (c = 1)
• Why? GW experiments such as VIRGO/LIGO
need high order corrections for detection (phase).
• Several techniques available to calculate PN
corrections, UV divergences.
Friday, September 17, 2010
17. EFT method
• UV divergences due to field theory coupled to
point-particles.
• Reformulation of PN corrections in terms of
Feynman diagrams hep-th/0409156
• NRGR : binary inspiral as at EFT calculation
Track this contribution in observables.
Friday, September 17, 2010
18. III. Tools: NRGR Tutorial
• “Non relativistic General Relativity”
• Translates PN corrections of N-body (binary)
systems into Feynman diagrams.
• Powerful toolbox of EFT techniques (UV
divergences), manifest power-counting.
Friday, September 17, 2010
19. Main Ingredients of NRGR
• Identify relevant dof at the scale of interest.
gµν , x (λ)
µ
• Construct effective Lagrangian allowed by
µ
symmetries. GCI :x → x (x)
µ
Worldline RPI :λ → λ (λ)
• Separate into conservative gravitons H
and radiative gravitons h
• Identify how terms scale in powers of v
• Collect Feynman diagrams to desired powers in v
Friday, September 17, 2010
20. Relevant Scales of a Binary System
We want two EFTs,
one at the orbital scale of the binary,
the other at the scale of radiation.
Friday, September 17, 2010
21. Starting point
Theory of relativistic point particles coupled to gravity:
S = SEH + Spp
√
SEH =−2m2 l
P
4
d x gR(x)
Spp =− ma dτa + ... O(v 10 ) Finite size effect
Neglect spin
a
dτ 2 = gµν dxµ dxν
Friday, September 17, 2010
30. Tools
Basic Results in NRGR
The EIH Lagrangian
The potential Lagrangian (orbital scale)
1
L = L0 + L2
c2
1 2 1 2 Gm1 m2
L0 = m1 v1 + m2 v2 +
2 2 r
1 2 1 4 Gm1 m2
L2 = m1 v2 + m2 v2 +
8 8 2r
2 2 G(m1 + m2 )
× 3(v1 + v2 ) − 7v1 · v2 − (ˆ · v1 )(ˆ · v2 ) −
r r
r
The effective Lagrangian (conservative dynamics) valid to 1PN.
Friday, September 17, 2010
31. The 2PN Radiation Lagrangian
The 1PN radiation Lagrangian is identically zero in the CM. The
Radiation Scale EFT
2PN radiation Lagrangian is the next-to-leading correction :
v2
h00 1 2 Gm1 m2
Lrad = − ma va −
2MP l 2 a
r
1 1 O(v 5/2 )
− ijk Lk ∂j hi0 + ma rai raj R0i0j
2MP l 2MP l a
Friday, September 17, 2010
32. Tools
Basic Results in NRGR
Quadrupole Radiation Forumla
Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
Tools
Quadrupole Radiation (2.5PN)
Basic Results in NRGR
Quadrupole Radiation Forumla
2
1 1 1
Im −i 2MP l a,b dt1 dt2 Qij (t1 )Qkl (t2 ) R0i0j (t1 , Xcm )R0k0l (t2 , Xcm )
2
1 1 1
Im −i 2MP l a,b dt1 dt2 Qij (t1 )Qkl (t2 ) R0i0j (t1 , Xcm )R0k0l (t2 , Xcm )
GN ... ...
P = Q... Q
G5 ... ij ij
N
P = Qij Qij
5
where the quadrupole moment is defined by:
where the quadrupole moment is defined by:
1 12 2
Qij ij =
Q= ma rraiajaj −δij rδij ra
ma ai r r −
3 3a
aa
Friday, September 17, 2010
33. v2
The radiation Lagrangian (2.5PN)
h00 1 2 Gm1 m2
Lrad = − ma va −
2MP l 2 a
r
1 1
− ijk Lk ∂j hi0 + ma rai raj R0i0j
2MP l 2MP l a
The effective Lagrangian responsible for radiation to leading order.
Friday, September 17, 2010
34. Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
Tools
Basic Results in NRGR
NRGR in a nutshell
NRGR Summary
We saw:
The different length scales at hand (rs , r ∼ H, h)
How to build the NRGR EFT
How to get Lconservative with PN corrections
(Newton + EIH + ...)
How to get Lradiation with PN corrections.
More importantly, we have seen exactly how the 3- and 4- graviton
More importantly, wePN corrections. how the
vertices contribute to these have seen
three graviton vertex contributes to the
-1PN correction (EIH)
- quadrupole radiation
Friday, September 17, 2010
35. Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
Results
Modification of the 3-graviton vertex
IV. Measuring deviations (GR)
Modifying the 3g Vertex
arxiv:0907.2186v2
→ (1 + β3 )×
This factor will affect in particular the following diagrams HHH
and HHh:
(1 + β3 ) (1 + β3 )
Friday, September 17, 2010
36. Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
Results
Comparing with Classical Tests of GR
Estimating β3 :Estimating β3
Classical Tests (orbit)
By modifying the three-graviton vertex, we have modified the
conservative part of the Lagrangian:
Modification to the 1PN Lagrangian
G2 m1 m2 (m1 +m2 )
∆Lcons = −β3 N r2
In terms of PPN parameters, we can identify β = 1 + β3 and γ = 1.
Perihelion of Mercury
|β − 1| 3 · 10−3 −→ |β3 | 3 · 10−3
Lunar Laser Ranging
|4β − γ − 3| 9 · 10−4 −→ |β3 | 2 · 10−4
Friday, September 17, 2010
37. N
possible vertices, and we must Qij Qij the framework of multiscalar-tensor theories, the e
(17)
ction of
PQQ = G compute, the the PPN formalism introduced in Ref [11] a
in imaginary(22)
part of PQQ = 5 N Q Q , of
tension
··· ···
(22)
ij lows for a consistent treatment of both the conservati
ij
(18) 5
ith our as already found in [34]. Computingdynamics (including the effects. strongly self-gravitatin
4 the otherradiative case of
contribu-
−i bodies)band of
(18) a b a
tions 2 find thatdt2 I[34]. )Ikl (t2 ) Sij (t1 Pqq (t2 ) interesting to see what bounds on β3 ca
as already found in ijterms PQq andIt)Skl vanish(21)
we dt1 the (t1 Computing the other contribu-
is clearly , identi-
8MPl
Estimating β (radiation)
cally. In fact, the Qq and qQ graphs vanish becauseidenti- probe the radiati
tions we find that the terms PQq and Pqq vanishtheQij thatbinary pulsars or th
be obtained from experiments
(19) a,b=1
j
h(19)
3 sector of because δij δkl of of
GR, such as
cally. In fact, the qδ , and δqQβgraphs vanish on the Q
Qq β V , Z )observation because
timing
is traceless, while the qq graph vanishes of the coalescence ij compact binaries at i
ij )] , a
where Iij = (Qij , ij 3 ij 3 ij terferometers. The effective Lagrangian describing th
depends
is the gives zero when contracted δik δjl + vanishes2 δijh kl , on δij δkl
is traceless, while S a = graph δil δ , δ− 3 of, δij ) which
matter variables andthe qq (R0i0j , R0i0jjk ij h002 the binary system with radiation gravito
because
(16) interaction
is the tensor thatfield. ijWhenδboth the il δjk −bythefunctionthree graphs in Fig. 2 (co
the gravitational contracted from +is obtained 3 δij δdia-which
gives zero when comes out ik δmore complicated.
δ two-point kl ,
0i0i ,and
is is
rce the The R0k0l . The formula and V Z graphs Fig. 6 of ref.for and the introduction
R the
radiation QV , qZ is responding to vanish [34]),
jl vertices of computing the
0i0i ,=
β3 is gram in Fig. 3that proportionalfrom the two-pointone in Fig. 2c.
is 0i0j tensor are comes out to the 3quadrupole, vertex
β affects the HHh
function
similar R0k0l . The QV , qZ and V contributions come in ref. [34], but with o
obtains reasons, so the only relevant Z graphs vanish as
R0i0j the usual GR result Computing these graphs for
r orbit
β3 =
reorbit
the
(17) from thereasons, so the G ···and we find three-graviton vertex, we find
similar QZ and qV graphs, relevant contributions come
only ··· modified
N
cation
re the from the QZ andQQ =graphs, and ,we find1 [Qij R0i0j + qR0i0i + β3 (3V h00 + Z ij hij )]
P qV
5
Qij Qij
··· Lrad =
˙
(22)
PQZ = −2β3 GN Qij Zij , 2MPl (23)
cation(18) in ···
˙
as already found P [34]. ComputingQ where Qij is the quadrupole moment of the source an
theZ , contribu- (23)
other
(1
upled and QZ = −2β3 GN ij ij
tions we find that the terms PQq and weqq vanish identi-
P define
upled
oupled cally. In fact, the Qq and qQ graphs vanish because Qij 1
(19) and ··· ˙
PqV = −6β3 Gvanishes. because δ q = 3 ma x2 ,
terms
oupled is traceless, while the qq graph N qV (24) (1
ij δkl
a
a
··· ˙ 2 δ δ , which
)terms
is the
e can As for thewhen and ZZ= −6β3+they V 3 ij contributionm1 m2 ,
gives zero
V V contracted δik δjl Gδil δq give a kl V (r) = GN r
PqV graphs, N jk − . (24) (1
R0i0i , is is the tensor that comes out from the two-point function
that, from theVpoint of view of the multipole expansion,m1 m2 ri rj
As0i0j R0k0l . The QV , qZ and V Z graphs vanish(r) = GN 3
R for the V and ZZ graphs, they give a contribution
no same order .
ation
or β3 =
ce can Z ij for , (1
Note:thedipole radiationas the quadrupole radiation but pro- r
is of from the so the only relevant contributions expansion,
e orbit similar reasons, point of view of the multipole come
that,
uation
(20)
2
portional QZ β3 , and graphs, and we find r = x1 − x2 . The term Qij R0i0j in eq. (16) is th
to and qV can be neglected. where
from the same order as the quadrupole radiation but pro-
are the is of the
We can now use these results to perform the compari-The second term, qR0i0i ,
2
usual quadrupole interaction.
fication
(20) portional to β3 , and can be neglected.
···
˙ ijnon-radiating when β3 =radiated powersee thatthe orb
0, but we will for β3
he or- son with binary QZ = −2β3 GN Qij Z 0 it contributes to(23)
P pulsars and with interferometers. the
, when
We can now use these results to isperform the compari- in eq. (16) are th
non-circular. The last two terms
on for
coupled 17,and
Friday, September 2010 explicit β3 -dependent terms induced by the modificatio
38. Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
Results
Comparing with the Hulse-Taylor Binary
The Hulse-Taylor Binary Pulsar
Estimating inβ3
Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
The Hulse-Binary Pulsar was first detected 1974.
Results
Modification of the 3-graviton vertex
The classical GR results for the period slow-down is:
Calculating the Power
Period Slow-Down
Plugging in the Newtonian equations of motion for elliptic orbits,
˙
P GR GR −8/3
Pb
96 5/3
we have: 5/3
b
GR
Pb
= − 5 GN ν M 2π [f (e)]
32G4 µ2 M 3 1 73 37
PQQ = N
1 + e2 + e4 ,
5a5 (1 − e2 )7/2 24 96
32G4 µ2 M 3 1 5 175 85
PQZ = β3period5 as calculated with the2 modified,
The slow-down
N
+ e + e4
5a (1 − e2 )7/2 2 24 96
three-graviton vertex:4 µ2 M 3
32GN 1 5 2 5
˙β PqV = −β3 β
β3−8/3 2 7/2 e + e4 .
Pb 96 5/3 5a5 Pb
5/3 (1 − e ) 16 64
β =− 5 GN ν M 2π [f (e) + β3 g(e)]
Pb
What M =can + m2extract m1 m2 /M 2
information m1 we ν = from this? M1 M2
˙β ˙ ν=
0≤e Pb = 0 P GR .
Compare≤ 1, ewithfor bcicular orbits. M
M = M1 + M2
Friday, September 17, 2010
39. Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pu
acting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
esults Results
Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
Comparing with the Hulse-Taylor Binary Comparing with the Hulse-Taylor Binary
Results
Comparing with the Hulse-Taylor Binary
stimating β3 Estimating β33
Estimating β
Estimating β3
The total mass M
(Tentative(Tentative are
andcalculations.) Replacing M → Mβ and ν M ν→
the ratio ν calculations.) Replacing → β
determined by the
˙1β / β GR
˙˜
PbβωP GR = Pb + P3 g (e) = 1 +
periastron shift˙ /˙
and the Einstein
where g (e) 2.70gfor the Hulse-Binary Pulsar.
˜ where ˜(e)
time delay γ. The 2.70 for the Hulse-Binary
Compared to experiment: ωβ3 = (1
point is that these experiment:− β3 /3) ωGR
Compared to
ng the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries ˙
Pbobs /PbGR γβ3 = 1
two parameters = 1.0013(21) γGR + 2.70β3
˙
ts
˙
˙ obs M 3 = = 1.0013(21)
are in principle Pb /PβGR (1 + β3 /2) MGR
mparing with the Hulse-Taylor Binary b
we get: modified by β3 . νβ3 = (1 + Cβ3 )νGR
mating β3 we get:
Hulse-Taylor → β3
(Tentative calculations.) Replacing M → Mβ and ν → νβ Hulse-Taylor
we get, → β3
Pbβ /P GR = 1 + β3 g (e)
˙ ˙ ˜
β3 = (4.0 ± 6.4) · 10−4
where g (e) 2.70 for the Hulse-Binary Pulsar.
˜
Compared to experiment: β3 = (4.0 ± 6.4) · 10
˙ ˙
Pbobs /PbGR = 1.0013(21) 1 + 2.70β3
we get:
Friday, September 17, 2010
40. Interpretation
• Radiation from Hulse-Taylor binary pulsar provides
measurement of the gauge structure of GR (0.1%).
• Assumes that GR is the low-energy limit of a high-
energy theory gravity, then experimental accuracy
provides bounds on possible deviations generated
by new physics.
Friday, September 17, 2010
41. Not the end of the story...
• If GR is not the correct low-energy EFT,
could have different bounds.
Friday, September 17, 2010