Tarun Souradeep

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Cosmology the perturbed universe
1st Asian Winter School Pheonix Park, Korea (Jan
16, 2007)
Tarun Souradeep
I.U.C.A.A, Pune, India
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How do we know so much now about this model
Universe ?
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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)
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Cosmic SuperIMAX theater
0.5 Myr
14 GPc
Here Now (14 Gyr)
Transparent universe
Opaque universe
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Universe is not smooth now
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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
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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
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Statistics of CMB
CMB Anisotropy Sky map gt Spherical Harmonic
decomposition

Gaussian CMB anisotropy completely specified by
the angular power spectrum IF
Statistical isotropy
(gt Correlation function C(n,n)hDT DTi is
rotationally invariant)
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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.
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Dissected CMB power spectrum

• Moderate multipole Acoustic Doppler peaks

• High multipole Damping tail

• Low multipole Sachs-Wolfe plateau

CMB physics is very well understood !!!
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Music of the Cosmic Drum
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Ping the Cosmic drum
More technically, the Green function
(Fig Einsentein )
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Perturbed universe superposition of random
pings
(Fig Einsentein )
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Ripples in the different constituents
(Einsentein et al. 2005)
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Angular power spectrum
Sensitive to curvature
FigHu Dodelson 2002
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Angular power spectrum
Sensitive to Baryon density
FigHu Dodelson 2002
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Estimating the Angular Power spectrum
(Souradeep 1998)
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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
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Post-COBE Ground Balloon Experiments
Python-V 1999, 2003
Boomerang 1998
DASI 2002 (Degree Angular scale Interferometer)
Archeops 2002
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Highlights of CMB Anisotropy Measurements (1992-
2002)
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First NASA CMB Satellite mission
Second NASA CMB Satellite mission
2003
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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
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WMAP Full sky coverage
30 sky daily, Whole sky every 6 months
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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
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WMAP map of CMB anisotropy
-200 ? K lt ? T lt 200 ? K ? Trms ¼ 70? K
CMB temperature Tcmb 2.725 K
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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
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Peaks of the angular power spectrum
(Saha, Jain, Souradeep Apj Lett 2006)
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Controlling other Systematics Eg.,Non-circular
beam effect in CMB measurements
(S. Mitra, A. Sengupta, Souradeep, PRD 2004)
WMAP Q beam
Eccentricity 0.7
Close to the corrections in the WMAP 2nd data
release (Hinshaw et al. 2006)
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PDF of Angular spectrum
For power at an individual multipole

• Chi-square distribution with (2l1) degrees of
  freedom.
• Non-Gaussian probability distribution ?
  Gaussian at large multipoles

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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)
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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).
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SLOAN DIGITAL SKY SURVEY (SDSS)
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Gravitational Instability
Mildly Perturbed universe at z1100
Present universe at z0
Cosmic matter content
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Gravitational Instability
Time ?
Cosmological constant cold dark matter
Standard cold dark matter
( now )
(quarter size )
(half size)
expansion ?
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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.
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Power spectrum of mass distribution
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Sensitivity to curvature
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Sensitivity to Dark energy fraction
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Sensitivity to Dark matter fraction
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Sensitivity to Baryonic matter fraction
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Cmbgg OmOl
CMB

LSS
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Weighing the Neutrinos
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Cosmological constraints on n mass
3-n degenerate mass Wn 3 mn /(94.0 eV) fn
Wn/WDM
(95 CL)
mn lt 1.0 eV
mn lt 0.4 eV
mn lt 0.16 eV
(MacTavish et al. astro-ph/0507503)
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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
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Good old Cosmology, New trend !
Total energy density
Dark energy density
Baryonic matter density
Dawn of Precision cosmology !!
NASA/WMAP science team