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Transcript of Tarun Souradeep
Tarun SouradeepI.U.C.A.A, Pune, India 1st Asian Winter SchoolPheonix Park, Korea(Jan 16, 2007)Cosmology: the perturbed universe
How do we know so much now about this model Universe ?
Post-recombination :Freely propagating through (weakly perturbed) homogeneous & isotropic cosmos.Pre-recombination : Tightly coupled to, and in thermal equilibrium with, ionized matter.
Pristine relic of a hot, dense & smooth early universe - Hot Big Bang model(text background: W. Hu)Cosmic Microwave Background
Cosmic SuperIMAX theater Transparent universeOpaque universe14 GPcHere & Now(14 Gyr)0.5 Myr
Universe is not smooth now
After 25 years of intense search, tiny variations (~10 p.p.m.) of CMB temperature sky map finally discovered. Holy grail of structure formation Predicted as precursors to the observed large scale structure
Cosmic Microwave Background a probe beyond the cosmic horizonPre-recombination : Tightly coupled to, and in thermal equilibrium with, ionized matter.Post-recombination :Freely propagating through (weakly perturbed) homogeneous & isotropic cosmos.Pristine relic of a hot, dense & smooth early universe - Hot Big Bang modelCMB 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
CMB Anisotropy Sky map => Spherical Harmonic decomposition Statistics of CMBStatistical isotropy Gaussian CMB anisotropy completely specified by theangular power spectrum IF(=> Correlation function C(n,n)=hDT DTi is rotationally invariant)
The Angular power spectrum of CMB anisotropy is considered a powerful tool for constraining cosmological parameters.Fig. M. White 1997The Angular power spectrum of the CMB anisotropy dependssensitively on the present matter current of the universe and the spectrum of primordial perturbations
Low multipole : Sachs-Wolfe plateau Moderate multipole : Acoustic Doppler peaks High multipole : Damping tail CMB physics is verywell understood !!!
Music of the Cosmic Drum
Ping the Cosmic drum More technically,the Green function (Fig: Einsentein )
Perturbed universe: superposition of random `pings (Fig: Einsentein )
Ripples in the different constituents (Einsentein et al. 2005)
Fig:Hu & Dodelson 2002Sensitive to curvature
Fig:Hu & Dodelson 2002Sensitive to Baryon density
Cosmic Variance of the unbiased estimatorNoise term dominates beyond beam widthcrude account of incomplete skyHomo. , Uncorrelated noise:Gaussian beam :Inevitable error for one sky
Boomerang 1998 DASI 2002 (Degree Angular scale Interferometer) Archeops 2002Python-V 1999, 2003 Post-COBE Ground & Balloon Experiments
Highlights of CMB Anisotropy Measurements (1992- 2002)
2003Second NASA CMB Satellite mission First NASA CMB Satellite mission
NASA : Launched July 2001Wilkinson Microwave Anisotropy Probe NASA/WMAP science teamWMAP: 1-year results announced on Feb, 2003 !WMAP: 3-year results announced on Mar, 2006 !
30% sky daily, Whole sky every 6 months
K band 23 GHzKa band 33 GHzQ band 41 GHzV band 61 GHzW band 94 GHzCMB anisotropy signalWMAP multi-frequency maps
-200 K < T < 200 K Trms 70 K CMB temperature Tcmb = 2.725 K
IIT Kanpur + IUCAAIndependent, self contained analysis of WMAP multi-frequency maps Blind estimation : no extraneous foreground info. ! I.e., free of uncertainty of foreground modelingSaha, Jain, Souradeep(Apj Lett 2006)Eriksen et al. ApJ. 2006
Peaks of the angular power spectrum(Saha, Jain, Souradeep Apj Lett 2006)
Controlling other SystematicsEg.,Non-circular beam effect in CMB measurements(S. Mitra, A. Sengupta, Souradeep, PRD 2004)WMAP Q beamEccentricity =0.7Close to the corrections in the WMAP 2nd data release(Hinshaw et al. 2006)
PDF of Angular spectrumChi-square distribution with (2l+1) degrees of freedom.Non-Gaussian probability distribution Gaussian at large multipoles For power at an individual multipole
Approximations: Gaussian : (Match peak and variance) BJK: Gaussian in
Equal variance: Np independent modes with equal variance (Bond, Jaffe & Knox)Approx. PDF for Band powers
Expand the Likelihood L(Cl) around the best fit valuesError covariance matrix How well are Parameters Estimated?Eigenvalues of Inverse Fisher matrix rank order the parameter combinations (Eigenmodes).
SLOAN DIGITAL SKY SURVEY (SDSS)
Mildly Perturbed universe at z=1100Present universe at z=0Gravitational Instability Cosmic matter content
Standard cold dark matterCosmological constant + cold dark matterGravitational Instability ( now )(quarter size )(half size)Time expansion
Measure the variance in the total mass var(M) enclosed in spheres of a given radius R thrown randomly in the cosmos.
Characterizing the mass distribution power spectrum Var(R) vs. R
Power spectrum of mass distribution
Sensitivity to curvature
Sensitivity to Dark energy fraction
Sensitivity to Dark matter fraction
Sensitivity to Baryonic matter fraction
Weighing the Neutrinos
(MacTavish et al. astro-ph/0507503)mn < 0.16 eV3-n degenerate massWn = 3 mn /(94.0 eV)fn= Wn/WDMmn < 0.4 eVmn < 1.0 eV (95% CL)Cosmological constraints on n mass
Baryonic matterDark matterExpansion rateDark energyCosmic ageMulti-parameter (7-11) joint estimation (complex covariance, degeneracies, priors, marginal distributions) Strategies to search & Locate best parameters: Markov Chain Monte CarloCosmological Parameters Optical depthFig.:R.Sinha, TS
NASA/WMAP science teamTotal energy density Baryonic matter density Dawn of Precision cosmology !!Dark energy density Good old Cosmology, New trend !