Cosmology with CMB: the perturbed universe Utkal Univ. (Jan 11-12, 2008) 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 GPc Transparent universe Opaque universe
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 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)
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.
Low multipole : Sachs-Wolfe plateau Moderate multipole : Acoustic Doppler peaks High multipole : Damping tail CMB physics is very well understood!!!
Cosmic Microwave Background X R H /33
Cosmic Super IMAX theater 0.5 Myr Here & Now (14 Gyr) 14 GPc Transparent universe Causal horizon c s τ rec Opaque universe
Music of the Cosmic Drum
Ping the Cosmic drum (Fig: Einsentein ) More technically, the Green function
Perturbed universe: superposition of random `pings (Fig: Einsentein )
(Einsentein et al. 2005) Ripples in the different constituents 150 Mpc.
Sensitive to curvature 1 Ω K l = 220 Fig:Hu & Dodelson 2002 l
Fig:Hu & Dodelson 2002 Sensitive to Baryon density ΔT = 74μK
(Souradeep 1998)
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
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: WMAP: 3-1- year year results results announced announced on on Mar, Feb, 2006 2003!! NASA/WMAP science team
30% sky daily, Whole sky every 6 months
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
CMB temperature T cmb = 2.725 K -200 μ K < Δ T < 200 μ K Δ T rms 70μ 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. ApJ. 2006
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)
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)
Ω +Ω +Ω +Ω + Ω +... = 1 0 0 0 0... 1 m DE K r r The Cosmic Triangle (Ostriker & Steinhardt) Ω = 0 0K
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)
Power spectrum of mass distribution
Gravitational Instability Time Cosmological constant + cold dark matter Standard cold dark matter (fig: Virgo simulations) (quarter size ) (half size) expansion ( now )
SLOAN DIGITAL SKY SURVEY (SDSS)
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 ( Tegmark et al. 2004) k eq : k eq τ eq =1
Sensitivity to curvature
Sensitivity to Baryonic matter fraction
Sensitivity to Dark energy fraction
Sensitivity to Dark matter fraction
CMB + Cmbgg OmOl LSS (credit: Tegmark)
Weighing the Neutrinos
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/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