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Tarun Souradeep

Cosmology: the perturbed universe. 1 st Asian Winter School Pheonix Park, Korea (Jan 16, 2007). Tarun Souradeep. I.U.C.A.A, Pune, India. How do we know so much now about this model Universe ?. Cosmic Microwave Background.

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Tarun Souradeep

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  1. Cosmology: the perturbed universe 1st Asian Winter School Pheonix Park, Korea (Jan 16, 2007) Tarun Souradeep I.U.C.A.A, Pune, India

  2. How do we know so much now about this model Universe ?

  3. Cosmic Microwave Background Pristine relic of a hot, dense & smooth early universe - Hot Big Bang model Post-recombination :Freely propagating through (weakly perturbed) homogeneous & isotropic cosmos. Pre-recombination : Tightly coupled to, and in thermal equilibrium with, ionized matter. (text background: W. Hu)

  4. Cosmic “Super–IMAX” theater 0.5 Myr 14 GPc Here & Now (14 Gyr) Transparent universe Opaque universe

  5. Universe is not smooth now

  6. Cosmic Microwave Background Anisotropy Predicted as precursors to the observed large scale structure After 25 years of intense search, tiny variations (~10 p.p.m.) of CMB temperature sky map finally discovered. “Holy grail of structure formation”

  7. Cosmic Microwave Background – a probe beyond the cosmic horizon Pristine relic of a hot, dense & smooth early universe - Hot Big Bang model Pre-recombination : Tightly coupled to, and in thermal equilibrium with, ionized matter. Post-recombination :Freely propagating through (weakly perturbed) homogeneous & isotropic cosmos. CMB anisotropy is related to the tiny primordial fluctuations which formed the Large scale Structure through gravitational instability Simple linear physics allows for accurate predictions Consequently a powerful cosmological probe

  8. Statistics of CMB CMB Anisotropy Sky map => Spherical Harmonic decomposition Gaussian CMB anisotropy completely specified by the angular power spectrum IF Statistical isotropy (=> Correlation function C(n,n’)=hDT DTi is rotationally invariant)

  9. Fig. M. White 1997 The Angular power spectrum of the CMB anisotropy depends sensitively on the present matter current of the universe and the spectrum of primordial perturbations The Angular power spectrum of CMB anisotropy is considered a powerful tool for constraining cosmological parameters.

  10. Dissected CMB power spectrum • Moderate multipole : Acoustic “Doppler” peaks • High multipole : Damping tail • Low multipole : Sachs-Wolfe plateau CMB physics is very well understood !!!

  11. Music of the Cosmic Drum

  12. Ping the ‘Cosmic drum’ More technically, the Green function (Fig: Einsentein )

  13. Perturbed universe: superposition of random `pings’ (Fig: Einsentein )

  14. 150 Mpc. Ripples in the different constituents (Einsentein et al. 2005)

  15. Angular power spectrum Sensitive to curvature Fig:Hu & Dodelson 2002

  16. Angular power spectrum Sensitive to Baryon density Fig:Hu & Dodelson 2002

  17. Estimating the Angular Power spectrum (Souradeep 1998)

  18. Estimating the Angular Power spectrum Cosmic Variance of the unbiased estimator Homo. , Uncorrelated noise: Inevitable error for one sky Gaussian beam : Noise term dominates beyond beam width crude account of incomplete sky

  19. Post-COBE Ground & Balloon Experiments Python-V 1999, 2003 Boomerang 1998 DASI 2002 (Degree Angular scale Interferometer) Archeops 2002

  20. Highlights of CMB Anisotropy Measurements (1992- 2002)

  21. First NASA CMB Satellite mission Second NASA CMB Satellite mission 2003

  22. CMB space mission : WMAP Wilkinson Microwave Anisotropy Probe NASA : Launched July 2001 WMAP: 3-year results announced on Mar, 2006 ! WMAP: 1-year results announced on Feb, 2003 ! NASA/WMAP science team

  23. WMAP: Full sky coverage 30% sky daily, Whole sky every 6 months

  24. WMAP multi-frequency maps Ka band 33 GHz K band 23 GHz CMB anisotropy signal Q band 41 GHz W band 94 GHz V band 61 GHz

  25. WMAP map of CMB anisotropy -200  K <  T < 200  K  Trms¼ 70 K CMB temperature Tcmb = 2.725 K

  26. WMAP: Angular power spectrum Independent, self contained analysis of WMAP multi-frequency maps Blind estimation : no extraneous foreground info. ! I.e., free of uncertainty of foreground modeling IIT Kanpur + IUCAA Saha, Jain, Souradeep (Apj Lett 2006) Eriksen et al. ApJ. 2006

  27. (74.10.3, 219.80.8) (74.7 0.5, 220.1 0.8 (48.3 1.2, 544 17) (48.8 0.9, 546 10) (41.7 1.0, 419.2 5.6) (41.0  0.5, 411.7 3.5) Peaks of the angular power spectrum (Saha, Jain, Souradeep Apj Lett 2006)

  28. Controlling other Systematics Eg.,Non-circular beam effect in CMB measurements WMAP Q beam Eccentricity =0.7 (S. Mitra, A. Sengupta, Souradeep, PRD 2004) Close to the corrections in the WMAP 2nd data release (Hinshaw et al. 2006)

  29. PDF of Angular spectrum For power at an individual multipole • Chi-square distribution with (2l+1) degrees of freedom. • Non-Gaussian probability distribution  Gaussian at large multipoles

  30. Approx. PDF for Band powers • Approximations: • Gaussian : (Match peak and variance) • BJK: Gaussian in • WMAP: • Equal variance: Np independent modes with equal variance (Bond, Jaffe & Knox)

  31. How well are Parameters Estimated? Expand the Likelihood L(Cl) around the best fit values Error covariance matrix Eigenvalues of Inverse Fisher matrix rank order the parameter combinations (Eigenmodes).

  32. SLOAN DIGITAL SKY SURVEY (SDSS)

  33. Gravitational Instability Mildly Perturbed universe at z=1100 Present universe at z=0 Cosmic matter content

  34. Gravitational Instability Time  Cosmological constant + cold dark matter Standard cold dark matter (quarter size ) (half size) ( now ) expansion 

  35. Characterizing the mass distribution “power spectrum” Var(R) vs. R Measure the variance in the total mass var(M) enclosed in spheres of a given radius R thrown randomly in the cosmos.

  36. Power spectrum of mass distribution

  37. Sensitivity to curvature

  38. Sensitivity to Dark energy fraction

  39. Sensitivity to Dark matter fraction

  40. Sensitivity to Baryonic matter fraction

  41. Cmbgg OmOl CMB + LSS

  42. Weighing the Neutrinos

  43. Cosmological constraints on n mass • 3-ndegenerate mass • Wn = 3 mn /(94.0 eV) • fn= Wn/WDM (95% CL) mn < 1.0 eV mn < 0.4 eV mn < 0.16 eV (MacTavish et al. astro-ph/0507503)

  44. Cosmological Parameters Multi-parameter (7-11) joint estimation (complex covariance, degeneracies, priors,…  marginal distributions) Strategies to search & Locate best parameters: Markov Chain Monte Carlo Dark energy Cosmic age Dark matter Optical depth Baryonic matter Expansion rate Fig.:R.Sinha, TS

  45. Good old Cosmology, … New trend ! Total energy density Dark energy density Baryonic matter density Dawn of Precision cosmology !! NASA/WMAP science team

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