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Search for evidences beyond the
concordance model of cosmology
Arman Shafieloo
Korea Astronomy and Space Science Institute...
Era of Precision Cosmology
Combining theoretical works with new measurements and
using statistical techniques to place sha...
Standard Model of Cosmology
Using measurements and statistical techniques to place
sharp constraints on parameters of the ...
Standard Model of Cosmology
Using measurements and statistical techniques to place
sharp constraints on parameters of the ...
Standard Model of Cosmology
Using measurements and statistical techniques to place
sharp constraints on parameters of the ...
Beyond the Standard
Model of Cosmology
•  The universe might be more complicated than its
current standard model (Vanilla ...
Standard Model of Cosmology
Universe is Flat
Universe is Isotropic
Universe is Homogeneous
Dark Energy is Lambda (w=-1)
Po...
Planck 2015: No detectable primordial G-waves
Cosmological Parameters from
Planck [LCDM]
Planck Collaboration, Ade et al, A&A 594, A13 (2016)
Parameter estimation within a
cosmological framework
Tables from NASA - LAMBDA website
Harisson-Zel’dovich (HZ) Power-Law ...
Parameter estimation within a cosmological framework
Tables from NASA - LAMBDA website
Harisson-Zel’dovich (HZ) Power-Law ...
Early Universe affect the Late Universe!
Dark Energy Reconstruction
•  Uncertainties in matter density is bound to affect ...
Primordial Power
Spectrum
Detected by observation
Determined by background model
and cosmological parameters
Suggested by ...
Primordial Power
Spectrum
Detected by observation
Determined by background model
and cosmological parameters
Suggested by ...
Primordial Power
Spectrum
Detected by observation
Determined by background model
and cosmological parameters
Reconstructed...
Primordial Power Spectrum from Planck
Hazra, Shafieloo & Souradeep, JCAP 2014
Cosmological Parameter Estimation with
Power-Law Primordial Spectrum
•  Flat Lambda Cold Dark Matter Universe (LCDM)
with ...
Cosmological Parameter Estimation with
Free form Primordial Spectrum
Cl = G(l,k)P(k)∑
G(l,k)
P(k)Cl
obs
2
2
3
3
4
1
Direct...
Cosmological Parameter Estimation
with Free form Primordial Spectrum
Red Contours:
Power Law PPS
Blue Contours:
Free Form ...
Beyond Power-Law:
there are some other
models consistent to
the data.
Hazra, Shafieloo, Smoot, JCAP 2013
Hazra, Shafieloo,...
Beyond Power-Law:
there are some other
models consistent to
the data.
Hazra, Shafieloo, Smoot, JCAP 2013
Hazra, Shafieloo,...
Plausible approach for the future:
Joint constraint on inflationary features using the two and three-
point correlations o...
From 2D to 3D (first steps)
- Generating many N-body simulations (similar to stage IV
dark energy measurements such as DES...
From 2D to 3D
N-Body Simulation (DESI like)
L’Huillier & Shafieloo (in prep)
Standard Model of Cosmology
Universe is Flat
Universe is Isotropic
Universe is Homogeneous (large scales)
Dark Energy is L...
D. Sherwin et.al, PRL 2011
Accelerating Universe, Now
Hazra, Shafieloo, Souradeep, PRD 2013
Free PPS, No H0 Prior
FLAT LCD...
Dark Energy Models
•  Cosmological Constant
•  Quintessence and k-essence (scalar fields)
•  Exotic matter (Chaplygin gas,...
To find cosmological quantities and parameters
there are two general approaches:
1.  Parametric methods
Easy to confront w...
Problems of Dark Energy Parameterizations
(model fitting)
Holsclaw et al, PRD 2011Shafieloo, Alam, Sahni &
Starobinsky, MN...
Cosmographic Degeneracy
Full theoretical picture:
•  Cosmographic Degeneracies would make it so hard to
pin down the actual model of dark energy even in the
near future.
In...
Reconstruction & Falsification
Considering (low) quality of the data and
cosmographic degeneracies we should
consider a ne...
•  Instead of looking for w(z) and exact
properties of dark energy at the current
status of data, we can concentrate on a
...
Om diagnostic
V. Sahni, A. Shafieloo, A. Starobinsky,
PRD 2008
We Only Need h(z)
Om(z) is constant only
for FLAT LCDM mode...
SDSS III Collaboration
L. Samushia et al, MNRAS 2013
WiggleZ collaboration
C. Blake et al, MNRAS 2011
SDSS III DR-12 / BOS...
Omh2(z1, z2 ) =
H2
(z2 )− H2
(z1)
(1+ z2 )3
−(1+ z1)3
= Ω0mH2
0
Omh2
Model Independent Evidence for Dark Energy Evolution
...
Omh2(z1, z2 ) =
H2
(z2 )− H2
(z1)
(1+ z2 )3
−(1+ z1)3
= Ω0mH2
0
Omh2
Model Independent Evidence for Dark Energy Evolution
...
Omh2(z1, z2 ) =
H2
(z2 )− H2
(z1)
(1+ z2 )3
−(1+ z1)3
= Ω0mH2
0
Omh2
Model Independent Evidence for Dark Energy Evolution
...
Omh2(z1, z2 ) =
H2
(z2 )− H2
(z1)
(1+ z2 )3
−(1+ z1)3
= Ω0mH2
0
Omh2
Model Independent Evidence for Dark Energy Evolution
...
Omh2(z1, z2 ) =
H2
(z2 )− H2
(z1)
(1+ z2 )3
−(1+ z1)3
= Ω0mH2
0
What if we combine many different cosmology data?
Should w...
arXiv:1701.08165
For LCDM; H0, LyFB and JLA measurements are in tension with
the combined dataset, with tension values of ...
arXiv:1701.08165
For LCDM; H0, LyFB and JLA measurements are in tension with
the combined dataset, with tension values of ...
arXiv:1701.08165
For LCDM; H0, LyFB and JLA measurements are in tension with
the combined dataset, with tension values of ...
arXiv:1701.08165
For LCDM; H0, LyFB and JLA measurements are in tension with
the combined dataset, with tension values of ...
Future perspective
Aghamousa et al, [arXiv:1611.00036] DESI Collaboration
Future perspective
Aghamousa et al, [arXiv:1611.00036] DESI Collaboration
Standard Model of Cosmology
Universe is Flat
Universe is Isotropic
Universe is Homogeneous (large scales)
Dark Energy is L...
Falsification:
Is Universe Isotropic?
Colin, Mohayaee, Sarkar & Shafieloo MNRAS 2011
Method of Smoothed Residuals
!Residua...
Method of Smoothed
Residuals is well
received and was used
recently by Supernovae
Factory collaboration
Bias in the Sky
Appleby, Shafieloo, JCAP 2014
Appleby, Shafieloo, Johnson, ApJ 2015
Method of
Smoothed
Residuals
Bias Cont...
Falsification:
Testing Isotropy of the Universe in Matter Dominated Era through
Lyman Alpha forest
Hazra and Shafieloo, JC...
Falsification:
Test of Statistical Isotropy in CMB
Akrami, Fantaye, Shafieloo, Eriksen, Hansen, Banday, Gorski, ApJ L 2014...
Curvature and Metric Test
by combining observables
of SN and BAO data
L’Huillier and Shafieloo, JCAP 2017
Shafieloo & Clar...
Testing deviations from an assumed model
(without comparing different models)
Gaussian Processes:
Modeling of the data aro...
Gaussian Process
Shafieloo, Kim & Linder, PRD 2012
Shafieloo, Kim & Linder, PRD 2013
èEfficient in statistical modeling of...
Detection of the features in the residuals
Signal
Detectable
Signal
Undetectable
Simulations
Simulations
GP to test GR
Cos...
GP Reconstruction of
Planck TT, TE, EE spectra
Aghamousa, Hamann & Shafieloo, JCAP 2017
Planck 2015
Testing GP
Aghamousa, Hamann & Shafieloo, JCAP 2017
GP Reconstruction of
Planck TT, TE, EE spectra
Aghamousa, Hamann & Shafieloo, JCAP 2017
GP Reconstruction of
Planck TT, TE, EE spectra
Aghamousa, Hamann & Shafieloo, JCAP 2017
excellent agreement between Planck...
Crossing Statistic (Bayesian Interpretation)
Crossing functionTheoretical model
Chebishev Polynomials
as Crossing Function...
Crossing Statistic (Bayesian Interpretation)
Crossing functionTheoretical model
Confronting the concordance model of cosmo...
Crossing Statistic (Bayesian Interpretation)
Crossing functionTheoretical model
Confronting the concordance model of cosmo...
Planck 2015:
No feature but interesting effect on background parameters.
Crossing
Statistics
Shafieloo & Hazra
JCAP 2017
Planck 2015:
No feature but interesting effect on background parameters.
Crossing
Statistics
Planck polarization data and ...
Beyond the Standard
Model of Cosmology?
•  Finding features in the data beyond the flexibility of the standard
model using...
Conclusion
•  The current standard model of cosmology seems to work fine but this
does not mean all the other models are w...
Conclusion (Large Scales)
•  We can (will) describe the constituents and
pattern of the universe (soon). But still we do
n...
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Ecl astana 28_september_2017_shrt

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Ecl astana 28_september_2017_shrt

  1. 1. Search for evidences beyond the concordance model of cosmology Arman Shafieloo Korea Astronomy and Space Science Institute (KASI) University of Science and Technology (UST) ECL science seminar, 28 September 2017 Nazarbayev University, Astana, Kazakhstan
  2. 2. Era of Precision Cosmology Combining theoretical works with new measurements and using statistical techniques to place sharp constraints on cosmological models and their parameters. Initial Conditions: Form of the Primordial Spectrum and Model of Inflation and its Parameters Dark Energy: density, model and parameters Dark Matter: density and characteristics Baryon density Neutrino species, mass and radiation density Curvature of the Universe Hubble Parameter and the Rate of Expansion Epoch of reionization
  3. 3. Standard Model of Cosmology Using measurements and statistical techniques to place sharp constraints on parameters of the standard cosmological model. Initial Conditions: Form of the Primordial Spectrum is Power-law Dark Energy is Cosmological Constant: Dark Matter is Cold and weakly Interacting: Baryon density Neutrino mass and radiation density: fixed by assumptions and CMB temperature Universe is Flat Hubble Parameter and the Rate of Expansion Epoch of reionization Ωb Ωdm ΩΛ =1−Ωb −Ωdm ns , As τ H0
  4. 4. Standard Model of Cosmology Using measurements and statistical techniques to place sharp constraints on parameters of the standard cosmological model. Initial Conditions: Form of the Primordial Spectrum is Power-law Dark Energy is Cosmological Constant: Dark Matter is Cold and weakly Interacting: Baryon density Neutrino mass and radiation density: assumptions and CMB temperature Universe is Flat Hubble Parameter and the Rate of Expansion Epoch of reionization Ωb Ωdm ΩΛ =1−Ωb −Ωdm ns , As τ H0 Combination of Assumptions
  5. 5. Standard Model of Cosmology Using measurements and statistical techniques to place sharp constraints on parameters of the standard cosmological model. Initial Conditions: Form of the Primordial Spectrum is Power-law Dark Energy is Cosmological Constant: Dark Matter is Cold and weakly Interacting: Baryon density Neutrino mass and radiation density: assumptions and CMB temperature Universe is Flat Hubble Parameter and the Rate of Expansion Epoch of reionization Ωb Ωdm ΩΛ =1−Ωb −Ωdm ns , As τ H0 combination of reasonable assumptions, but…..
  6. 6. Beyond the Standard Model of Cosmology •  The universe might be more complicated than its current standard model (Vanilla Model). •  There might be some extensions to the standard model in defining the cosmological quantities. •  This needs proper investigation, using advanced statistical methods, high performance computational facilities and high quality observational data.
  7. 7. Standard Model of Cosmology Universe is Flat Universe is Isotropic Universe is Homogeneous Dark Energy is Lambda (w=-1) Power-Law primordial spectrum (n_s=const) Dark Matter is cold All within framework of FLRW (Present)t
  8. 8. Planck 2015: No detectable primordial G-waves
  9. 9. Cosmological Parameters from Planck [LCDM] Planck Collaboration, Ade et al, A&A 594, A13 (2016)
  10. 10. Parameter estimation within a cosmological framework Tables from NASA - LAMBDA website Harisson-Zel’dovich (HZ) Power-Law (PL) PL with Running (RN)
  11. 11. Parameter estimation within a cosmological framework Tables from NASA - LAMBDA website Harisson-Zel’dovich (HZ) Power-Law (PL) PL with Running (RN) Functional parameterizations affect estimation of cosmological parameters Why form of the PPS is important?
  12. 12. Early Universe affect the Late Universe! Dark Energy Reconstruction •  Uncertainties in matter density is bound to affect the reconstructed w(z). H(z) = d dz dL (z) 1+ z ! " # $ % & ' ( ) * + , −1 Shafieloo et al, MNRAS 2006 ; Shafieloo MNRAS 2007 Sahni, Shafieloo & Starobinsky, PRD 2008 Shafieloo & Linder, PRD 2011 Cosmographic Degeneracy
  13. 13. Primordial Power Spectrum Detected by observation Determined by background model and cosmological parameters Suggested by Model of Inflation € Cl = G(l,k)P(k)∑ Cosmological Radiative Transport Kernel ? Cl th vs Cl obs Angular power Spectrum ModelingParameterization and Model Fitting
  14. 14. Primordial Power Spectrum Detected by observation Determined by background model and cosmological parameters Suggested by Model of Inflation and the early universe € Cl = G(l,k)P(k)∑ Cosmological Radiative Transport Kernel ?We cannot anticipate the unexpected !! Cl th vs Cl obs Angular power Spectrum
  15. 15. Primordial Power Spectrum Detected by observation Determined by background model and cosmological parameters Reconstructed by Observations € Cl = G(l,k)P(k)∑ Cosmological Radiative Transport Kernel DIRECT TOP DOWN Reconstruction Cl th vs Cl obs Angular power Spectrum
  16. 16. Primordial Power Spectrum from Planck Hazra, Shafieloo & Souradeep, JCAP 2014
  17. 17. Cosmological Parameter Estimation with Power-Law Primordial Spectrum •  Flat Lambda Cold Dark Matter Universe (LCDM) with power–law form of the primordial spectrum •  It has 6 main parameters. Cl = G(l,k)P(k)∑ G(l,k) Cl obs 1 1 2 2 3 Direct Reconstruction of PPS and Theoretical Implication
  18. 18. Cosmological Parameter Estimation with Free form Primordial Spectrum Cl = G(l,k)P(k)∑ G(l,k) P(k)Cl obs 2 2 3 3 4 1 Direct Reconstruction of PPS and Theoretical Implication
  19. 19. Cosmological Parameter Estimation with Free form Primordial Spectrum Red Contours: Power Law PPS Blue Contours: Free Form PPS Hazra, Shafieloo & Souradeep, PRD 2013
  20. 20. Beyond Power-Law: there are some other models consistent to the data. Hazra, Shafieloo, Smoot, JCAP 2013 Hazra, Shafieloo, Smoot, Starobinsky, JCAP 2014A Hazra, Shafieloo, Smoot, Starobinsky, JCAP 2014B Hazra, Shafieloo, Smoot, Starobinsky, Phys. Rev. Lett 2014 Hazra, Shafieloo, Smoot, Starobinsky, JCAP 2016 Whipped Inflation
  21. 21. Beyond Power-Law: there are some other models consistent to the data. Hazra, Shafieloo, Smoot, JCAP 2013 Hazra, Shafieloo, Smoot, Starobinsky, JCAP 2014A Hazra, Shafieloo, Smoot, Starobinsky, JCAP 2014B Hazra, Shafieloo, Smoot, Starobinsky, Phys. Rev. Lett 2014 Hazra, Shafieloo, Smoot, Starobinsky, JCAP 2016 Whipped Inflation
  22. 22. Plausible approach for the future: Joint constraint on inflationary features using the two and three- point correlations of temperature and polarization anisotropies Bispectrum in terms of the reconstructed power spectrum and its first two derivatives Direct reconstruction of PPS from Planck Appleby, Gong, Hazra, Shafieloo, Sypsas, PLB 2016
  23. 23. From 2D to 3D (first steps) - Generating many N-body simulations (similar to stage IV dark energy measurements such as DESI) based on various inflationary scenarios with features in PPS (but still degenerate to be distinguished by CMB data). - Try to distinguish them by implementing/designing appropriate statistics comparing 3D distributions. (power spectrum, bi-spectrum etc may not work)
  24. 24. From 2D to 3D N-Body Simulation (DESI like) L’Huillier & Shafieloo (in prep)
  25. 25. Standard Model of Cosmology Universe is Flat Universe is Isotropic Universe is Homogeneous (large scales) Dark Energy is Lambda (w=-1) Power-Law primordial spectrum (n_s=const) Dark Matter is cold All within framework of FLRW (Present)t
  26. 26. D. Sherwin et.al, PRL 2011 Accelerating Universe, Now Hazra, Shafieloo, Souradeep, PRD 2013 Free PPS, No H0 Prior FLAT LCDM Non FLAT LCDM Power-Law PPS Union 2.1 SN Ia Compilation WiggleZ BAO Something seems to be there, but, What is it?
  27. 27. Dark Energy Models •  Cosmological Constant •  Quintessence and k-essence (scalar fields) •  Exotic matter (Chaplygin gas, phantom, etc.) •  Braneworlds (higher-dimensional theories) •  Modified Gravity •  …… But which one is really responsible for the acceleration of the expanding universe?!
  28. 28. To find cosmological quantities and parameters there are two general approaches: 1.  Parametric methods Easy to confront with cosmological observations to put constrains on the parameters, but the results are highly biased by the assumed models and parametric forms. 2. Non Parametric methods Difficult to apply properly on the raw data, but the results will be less biased and more reliable and independent of theoretical models or parametric forms. . Reconstructing Dark Energy
  29. 29. Problems of Dark Energy Parameterizations (model fitting) Holsclaw et al, PRD 2011Shafieloo, Alam, Sahni & Starobinsky, MNRAS 2006 Chevallier-Polarski-Linder ansatz (CPL).. Brane Model Kink Model Phantom DE?! Quintessence DE?!
  30. 30. Cosmographic Degeneracy Full theoretical picture:
  31. 31. •  Cosmographic Degeneracies would make it so hard to pin down the actual model of dark energy even in the near future. Indistinguishable from each other! Shafieloo & Linder, PRD 2011 Cosmographic Degeneracy
  32. 32. Reconstruction & Falsification Considering (low) quality of the data and cosmographic degeneracies we should consider a new strategy sidewise to reconstruction: Falsification. Yes-No to a hypothesis is easier than characterizing a phenomena. But, How? We should look for special characteristics of the standard model and relate them to observables.
  33. 33. •  Instead of looking for w(z) and exact properties of dark energy at the current status of data, we can concentrate on a more reasonable problem: OR NOT Falsification of Cosmological Constant Yes-No to a hypothesis is easier than characterizing a phenomena
  34. 34. Om diagnostic V. Sahni, A. Shafieloo, A. Starobinsky, PRD 2008 We Only Need h(z) Om(z) is constant only for FLAT LCDM model Quintessence w= -0.9 Phantom w= -1.1 Falsification: Null Test of Lambda
  35. 35. SDSS III Collaboration L. Samushia et al, MNRAS 2013 WiggleZ collaboration C. Blake et al, MNRAS 2011 SDSS III DR-12 / BOSS Collaboration Y. Wang et al, arXiv:1607.03154
  36. 36. Omh2(z1, z2 ) = H2 (z2 )− H2 (z1) (1+ z2 )3 −(1+ z1)3 = Ω0mH2 0 Omh2 Model Independent Evidence for Dark Energy Evolution from Baryon Acoustic Oscillation Sahni, Shafieloo, Starobinsky, ApJ Lett 2014 Only for LCDM LCDM +Planck+WP BAO+H0 H(z = 0.00) = 70.6 pm 3.3 km/sec/Mpc H(z = 0.57) = 92.4 pm 4.5 km/sec/Mpc H(z = 2.34) = 222.0 pm 7.0 km/sec/Mpc Introducing litmus tests of Lambda: Comparing direct observables assuming a model.
  37. 37. Omh2(z1, z2 ) = H2 (z2 )− H2 (z1) (1+ z2 )3 −(1+ z1)3 = Ω0mH2 0 Omh2 Model Independent Evidence for Dark Energy Evolution from Baryon Acoustic Oscillation Sahni, Shafieloo, Starobinsky, ApJ Lett 2014 Only for LCDM LCDM +Planck+WP BAO+H0 H(z = 0.00) = 70.6 pm 3.3 km/sec/Mpc H(z = 0.57) = 92.4 pm 4.5 km/sec/Mpc H(z = 2.34) = 222.0 pm 7.0 km/sec/Mpc Important discovery if no systematic in the SDSS Quasar BAO data
  38. 38. Omh2(z1, z2 ) = H2 (z2 )− H2 (z1) (1+ z2 )3 −(1+ z1)3 = Ω0mH2 0 Omh2 Model Independent Evidence for Dark Energy Evolution from Baryon Acoustic Oscillation Sahni, Shafieloo, Starobinsky, ApJ Lett 2014 Only for LCDM LCDM +Planck+WP BAO+H0 H(z = 0.00) = 70.6 pm 3.3 km/sec/Mpc H(z = 0.57) = 92.4 pm 4.5 km/sec/Mpc H(z = 2.34) = 222.0 pm 7.0 km/sec/Mpc No systematic yet found, Measurement of BAO correlations at z=2.3 with SDSS DR12 Ly-Forests Bautista et al, arXiv:1702.00176 2017
  39. 39. Omh2(z1, z2 ) = H2 (z2 )− H2 (z1) (1+ z2 )3 −(1+ z1)3 = Ω0mH2 0 Omh2 Model Independent Evidence for Dark Energy Evolution from Baryon Acoustic Oscillation Sahni, Shafieloo, Starobinsky, ApJ Lett 2014 Only for LCDM LCDM +Planck+WP BAO+H0 H(z = 0.00) = 70.6 pm 3.3 km/sec/Mpc H(z = 0.57) = 92.4 pm 4.5 km/sec/Mpc H(z = 2.34) = 222.0 pm 7.0 km/sec/Mpc No systematic yet found, Results Persistent! Measurement of BAO correlations at z=2.3 with SDSS DR12 Ly-Forests Bautista et al, arXiv:1702.00176 2017
  40. 40. Omh2(z1, z2 ) = H2 (z2 )− H2 (z1) (1+ z2 )3 −(1+ z1)3 = Ω0mH2 0 What if we combine many different cosmology data? Should we see evidence for deviation from Lambda? Sahni, Shafieloo, Starobinsky, ApJ Lett 2014 Only for LCDM LCDM +Planck+WP BAO+H0 H(z = 0.00) = 70.6 pm 3.3 km/sec/Mpc H(z = 0.57) = 92.4 pm 4.5 km/sec/Mpc H(z = 2.34) = 222.0 pm 7.0 km/sec/Mpc Measurement of BAO correlations at z=2.3 with SDSS DR12 Ly-Forests Bautista et al, arXiv:1702.00176
  41. 41. arXiv:1701.08165 For LCDM; H0, LyFB and JLA measurements are in tension with the combined dataset, with tension values of T = 4.4, 3.5, 1.7. LCDM w(z)CDM Kullback-Leibler (KL) divergence to quantify the degree of tension between different datasets assuming a model.
  42. 42. arXiv:1701.08165 For LCDM; H0, LyFB and JLA measurements are in tension with the combined dataset, with tension values of T = 4.4, 3.5, 1.7. LCDM w(z)CDM
  43. 43. arXiv:1701.08165 For LCDM; H0, LyFB and JLA measurements are in tension with the combined dataset, with tension values of T = 4.4, 3.5, 1.7. LCDM w(z)CDM Bautista et al, [1702.00176] Found no systematic/mistake in the previous measurement
  44. 44. arXiv:1701.08165 For LCDM; H0, LyFB and JLA measurements are in tension with the combined dataset, with tension values of T = 4.4, 3.5, 1.7. LCDM w(z)CDM Follin & Knox [1707.01175] Zhang et al, [1706.07573] Both agrees with Riess et al 2016 H0 measurement Bautista et al, [1702.00176] Found no systematic/mistake in the previous measurement
  45. 45. Future perspective Aghamousa et al, [arXiv:1611.00036] DESI Collaboration
  46. 46. Future perspective Aghamousa et al, [arXiv:1611.00036] DESI Collaboration
  47. 47. Standard Model of Cosmology Universe is Flat Universe is Isotropic Universe is Homogeneous (large scales) Dark Energy is Lambda (w=-1) Power-Law primordial spectrum (n_s=const) Dark Matter is cold All within framework of FLRW (Present)t
  48. 48. Falsification: Is Universe Isotropic? Colin, Mohayaee, Sarkar & Shafieloo MNRAS 2011 Method of Smoothed Residuals !Residual Analysis, !Tomographic Analysis, !2D Gaussian Smoothing, !Frequentist Approach !Insensitive to non-uniform distribution of the data
  49. 49. Method of Smoothed Residuals is well received and was used recently by Supernovae Factory collaboration
  50. 50. Bias in the Sky Appleby, Shafieloo, JCAP 2014 Appleby, Shafieloo, Johnson, ApJ 2015 Method of Smoothed Residuals Bias Control
  51. 51. Falsification: Testing Isotropy of the Universe in Matter Dominated Era through Lyman Alpha forest Hazra and Shafieloo, JCAP 2015 !Comparing statistical properties of the PDF of the Lyman-alpha transmitted flux in different patches !Different redshift bins and different signal to noise !Results for BOSS DR9 quasar sample Results consistent to Isotropy
  52. 52. Falsification: Test of Statistical Isotropy in CMB Akrami, Fantaye, Shafieloo, Eriksen, Hansen, Banday, Gorski, ApJ L 2014 Using Local Variance to Test Statistical Isotropy in CMB maps "Based on Crossing Statistic !Residual Analysis, !Real Space Analysis " Low Sensitivity to Systematics !2D Adaptive Gaussian Smoothing !Frequentist Approach
  53. 53. Curvature and Metric Test by combining observables of SN and BAO data L’Huillier and Shafieloo, JCAP 2017 Shafieloo & Clarkson, PRD 2010
  54. 54. Testing deviations from an assumed model (without comparing different models) Gaussian Processes: Modeling of the data around a mean function searching for likely features by looking at the the likelihood space of the hyperparameters. Bayesian Interpretation of Crossing Statistic: Comparing a model with its own possible variations. REACT: Risk Estimation and Adaptation after Coordinate Transformation Modeling the deviation
  55. 55. Gaussian Process Shafieloo, Kim & Linder, PRD 2012 Shafieloo, Kim & Linder, PRD 2013 èEfficient in statistical modeling of stochastic variables èDerivatives of Gaussian Processes are Gaussian Processes èProvides us with all covariance matrices Data Mean Function Kernel GP Hyper-parameters GP Likelihood
  56. 56. Detection of the features in the residuals Signal Detectable Signal Undetectable Simulations Simulations GP to test GR Cosmic Growth vs Expansion Shafieloo, Kim, Linder, PRD 2013
  57. 57. GP Reconstruction of Planck TT, TE, EE spectra Aghamousa, Hamann & Shafieloo, JCAP 2017 Planck 2015
  58. 58. Testing GP Aghamousa, Hamann & Shafieloo, JCAP 2017
  59. 59. GP Reconstruction of Planck TT, TE, EE spectra Aghamousa, Hamann & Shafieloo, JCAP 2017
  60. 60. GP Reconstruction of Planck TT, TE, EE spectra Aghamousa, Hamann & Shafieloo, JCAP 2017 excellent agreement between Planck data and the best-fit LCDM
  61. 61. Crossing Statistic (Bayesian Interpretation) Crossing functionTheoretical model Chebishev Polynomials as Crossing Functions Shafieloo. JCAP 2012 (a) Shafieloo, JCAP 2012 (b) Comparing a model with its own variations
  62. 62. Crossing Statistic (Bayesian Interpretation) Crossing functionTheoretical model Confronting the concordance model of cosmology with Planck 2013 data Hazra and Shafieloo, JCAP 2014 Consistent only at 2~3 sigma CL
  63. 63. Crossing Statistic (Bayesian Interpretation) Crossing functionTheoretical model Confronting the concordance model of cosmology with Planck 2015 data Shafieloo and Hazra, JCAP 2017 Completely Consistent
  64. 64. Planck 2015: No feature but interesting effect on background parameters. Crossing Statistics Shafieloo & Hazra JCAP 2017
  65. 65. Planck 2015: No feature but interesting effect on background parameters. Crossing Statistics Planck polarization data and local H0 measurements seems having irresolvable tension. Maybe either or both have systematic? If not, new physics might be the answer. Shafieloo & Hazra JCAP 2017
  66. 66. Beyond the Standard Model of Cosmology? •  Finding features in the data beyond the flexibility of the standard model using non-parametric reconstructions or using hyper-functions. •  Introducing theoretical/phenomenological models that can explain the data better (statistically significant) than the standard model. •  Finding tension among different independent data assuming the standard model (making sure there is no systematic). How to go Implementing well cooked statistical approaches to get the most out of the data is essential!
  67. 67. Conclusion •  The current standard model of cosmology seems to work fine but this does not mean all the other models are wrong. •  Using parametric methods and model fitting is tricky and we may miss features in the data. Non-parameteric methods of reconstruction can guide theorist to model special features. •  First target can be testing different aspects of the standard ‘Vanilla’ model. If it is not ‘Lambda’ dark energy or power-law primordial spectrum then we can look further. It is possible to focus the power of the data for the purpose of the falsification. Next generation of astronomical/ cosmological observations, (DESI, Euclid, SKA, LSST, WFIRST etc) will make it clear about the status of the concordance model. •  Combination of different cosmological data hints towards some tension with LCDM model. If future data continues the current trend, we may have some exciting times ahead!
  68. 68. Conclusion (Large Scales) •  We can (will) describe the constituents and pattern of the universe (soon). But still we do not understand it. Next challenge is to move from inventory to understanding, by the help of the new generation of experiments.

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