Cosmology the perturbed universe 1 st Asian Winter

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 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)

Cosmic “Super–IMAX” theater 0. 5 Myr Here & Now (14 Gyr) 14 Transparent universe Opaque universe c P G

Universe is not smooth now

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”

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

Statistics of 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’)=h. DT DTi is rotationally invariant)

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.

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

Music of the Cosmic Drum

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

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

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

Sensitive to curvature Fig: Hu & Dodelson 2002

Sensitive to Baryon density Fig: Hu & Dodelson 2002

(Souradeep 1998)

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

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

Highlights of CMB Anisotropy Measurements (1992 - 2002)

First NASA CMB Satellite mission 2003 Second NASA CMB Satellite mission

Wilkinson Microwave Anisotropy Probe NASA : Launched July 2001 WMAP: 3 -1 yearresults announcedon on Mar, Feb, 2006 2003!! NASA/WMAP science team

30% sky daily, Whole sky every 6 months

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

CMB temperature Tcmb = 2. 725 K -200 K < T < 200 K Trms ¼ 70 K

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. Ap. J. 2006

Peaks of the angular power spectrum (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) (Saha, Jain, Souradeep Apj Lett 2006)

Controlling other Systematics Eg. , Non-circular beam effect in CMB measurements WMAP Q beam Eccentricity =0. 7 Close to the corrections in the WMAP 2 nd data release (Hinshaw et al. 2006) (S. Mitra, A. Sengupta, Souradeep, PRD 2004)

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

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

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).

SLOAN DIGITAL SKY SURVEY (SDSS)

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

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

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.

Power spectrum of mass distribution

Sensitivity to curvature

Sensitivity to Dark energy fraction

Sensitivity to Dark matter fraction

Sensitivity to Baryonic matter fraction

CMB + LSS Cmbgg Om. Ol

Weighing the Neutrinos

Cosmological constraints on n mass 3 -n degenerate mass Wn = 3 mn /(94. 0 e. V) fn= Wn/WDM (95% CL) mn < 1. 0 e. V mn < 0. 4 e. V mn < 0. 16 e. V (Mac. Tavish et al. astro-ph/0507503)

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 Baryonic matter Expansion rate Optical depth Fig. : R. Sinha, TS

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