Cosmology with CMB: the perturbed universe

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1 Cosmology with CMB: the perturbed universe Utkal Univ. (Jan 11-12, 2008) Tarun Souradeep I.U.C.A.A, Pune, India

2 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

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 Here & Now (14 Gyr) 14 GPc Transparent universe Opaque universe

5 Universe is not smooth now

6 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 ΔT ( θ, φ ) = l a lm Y lm ( θ, φ ) l= 2 m= l Gaussian CMB anisotropy completely specified by the angular power spectrum IF Statistical isotropy * lm l ' m' l ll ' mm' a a = C δ δ (=> Correlation function C(n,n )=hδt ΔTi is rotationally invariant)

of primordial perturbations C l The Angular power

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 C l The Angular power spectrum of CMB anisotropy is considered a powerful tool for constraining cosmological parameters.

10 Low multipole : Sachs-Wolfe plateau Moderate multipole : Acoustic Doppler peaks High multipole : Damping tail CMB physics is very well understood!!!

11 Cosmic Microwave Background X R H /33

12 Cosmic Super IMAX theater 0.5 Myr Here & Now (14 Gyr) 14 GPc Transparent universe Causal horizon c s τ rec Opaque universe

13 Music of the Cosmic Drum

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

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

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

17 Sensitive to curvature 1 Ω K l = 220 Fig:Hu & Dodelson 2002 l

18 Fig:Hu & Dodelson 2002 Sensitive to Baryon density ΔT = 74μK

20 (Souradeep 1998)

21 Cosmic Variance of the unbiased estimator Homo., Uncorrelated noise: Inevitable error for one sky Gaussian beam : var ( ~ ) C B 2 = + l l crude account of incomplete sky ( 2l + 1) f θ sky C N l = [ C S σ 2 exp( l 2 2) ] 2 N 4π N pix σ 2 pix σ 2 ( θ ) = exp, = exp 2σ 2 θ, σθ = θfwhm 2σ 2 Bl l θ 2 8ln 2 1 σθ 2 N 1 Noise term dominates beyond beam width

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

23 Highlights of CMB Anisotropy Measurements ( )

24 First NASA CMB Satellite mission 2003 Second NASA CMB Satellite mission

25 Wilkinson Microwave Anisotropy Probe NASA : Launched July 2001 WMAP: WMAP: 3-1- year year results results announced announced on on Mar, Feb, !! NASA/WMAP science team

26 30% sky daily, Whole sky every 6 months

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

28 CMB temperature T cmb = K -200 μ K < Δ T < 200 μ K Δ T rms 70μ K

30 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

31 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 2 nd data release (Hinshaw et al. 2006)

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

33 Ω +Ω +Ω +Ω + Ω +... = m DE K r r The Cosmic Triangle (Ostriker & Steinhardt) Ω = 0 0K

34 Gravitational Instability Mildly Perturbed universe at z=1100 Present universe at z=0 Cosmic matter content Ω Ω Ω tot b DM Ω Λ H 0 (credit: Virgo simulations)

35 Power spectrum of mass distribution

36 Gravitational Instability Time Cosmological constant + cold dark matter Standard cold dark matter (fig: Virgo simulations) (quarter size ) (half size) expansion ( now )

37 SLOAN DIGITAL SKY SURVEY (SDSS)

38 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.

39 Power spectrum of mass distribution ( Tegmark et al. 2004) k eq : k eq τ eq =1

40 Sensitivity to curvature

41 Sensitivity to Baryonic matter fraction

42 Sensitivity to Dark energy fraction

43 Sensitivity to Dark matter fraction

44 CMB + Cmbgg OmOl LSS (credit: Tegmark)

46 Weighing the Neutrinos

47 Cosmological constraints on ν mass 3-ν degenerate mass Ω ν = 3 m ν /(94.0 ev) f ν = Ω ν /Ω DM m ν m ν m ν (95% CL) < 1.0 ev < 0.4 ev < 0.16 ev (MacTavish et al. astro-ph/ )

Cosmological Parameters Multi-parameter (7-11) joint estimation (complex covariance, degeneracies, priors, marginal distributions) Strategies to

48 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

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

Cosmology with CMB & LSS:

Cosmology with CMB & LSS: the Early universe VSP08 lecture 4 (May 12-16, 2008) Tarun Souradeep I.U.C.A.A, Pune, India Ω +Ω +Ω +Ω + Ω +... = 1 0 0 0 0... 1 m DE K r r The Cosmic Triangle (Ostriker & Steinhardt)