Tarun SouradeepI.U.C.A.A, Pune, India

1st Asian Winter School

Pheonix Park, Korea

(Jan 16, 2007)

Cosmology: Cosmology: the perturbed universethe 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 “Super–IMAX” theater

Transparent universe

Opaque universe

14 GPc

Here & Now(14 Gyr)

0.5 Myr

Universe is not smooth now 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 horizon

Pre-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 model

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

),(),(2

l

l

lmlmlmYaT

CMB Anisotropy Sky map => Spherical Harmonic decomposition

Statistics of CMB

Statistical isotropy

*' ' ' 'lm l m l ll mma a C

Gaussian CMB anisotropy completely specified by the

angular power spectrumangular power spectrum IF

(=> Correlation function C(n,n’)=hT Ti is rotationally invariant)

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

Fig. M. White 1997

The Angular power spectrum of the CMB anisotropy dependssensitively on the present matter current of the universe and the spectrum of primordial perturbations

lC

•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’ Ping the ‘Cosmic drum’

More technically,the Green function (Fig: Einsentein )

Perturbed universe: superposition of random `pings’

Perturbed universe: superposition of random `pings’

(Fig: Einsentein )

Ripples in the different constituents Ripples in the different constituents

150 Mpc.

(Einsentein et al. 2005)

Fig:Hu & Dodelson 2002

Sensitive to curvature

K1220l

l

Fig:Hu & Dodelson 2002

Sensitive to Baryon density

KT 74

(Souradeep 1998)

Cosmic Variance of the unbiased estimatorCosmic Variance of the unbiased estimator

2222

sky

)exp(12

2~var lC

flC N

Sll

Noise term dominates beyond

beam widthcrude account of incomplete sky

22pix

pix

4N

Nl

NC

Homo. , Uncorrelated noise:

Gaussian beam : fwhm22

2

2

2ln8

1 ,

2

1exp ,

2exp)(

lBB l

Inevitable error for one sky

Boomerang 1998

DASI 2002 (Degree Angular scale

Interferometer) Archeops 2002

Python-V 1999, 2003

Post-COBE Ground & Balloon Experiments Post-COBE Ground & Balloon Experiments

Highlights of CMB Anisotropy Measurements (1992- 2002) Highlights of CMB Anisotropy Measurements (1992- 2002)

2003 Second NASA CMB Satellite mission

First NASA CMB Satellite mission

NASA : Launched July 2001

Wilkinson Microwave Anisotropy Probe

NASA/WMAP science team

WMAP: 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 GHz

Ka band 33 GHz

Q band 41 GHz

V band 61 GHz

W band 94 GHz

CMB anisotropy signal

WMAP multi-frequency maps

-200 K < T < 200 KTrms ¼ 70 K

CMB temperature Tcmb = 2.725 K

IIT Kanpur + IUCAA

Independent, self contained analysis of WMAP multi-frequency maps Blind estimation : no extraneous foreground info. ! I.e., free of uncertainty of foreground modeling

Saha, Jain, Souradeep(Apj Lett 2006)Eriksen et al. ApJ. 2006

(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)

(74.10.3, 219.80.8)

(74.7 0.5, 220.1 0.8

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 beam Eccentricity =0.7

Close to the corrections in the WMAP 2nd data

release

(Hinshaw et al. 2006)

PDF of Angular spectrum

)(

])(exp[)(

2

12

1

2

1

2

1

l

xl

l

x

C

CxP

l

l

l

•Chi-square distribution with (2l+1) degrees of freedom.

•Non-Gaussian probability distribution Gaussian at large multipoles

For power at an individual multipole

l

lmlmlml aa

lC *~~

)12(

1~

Approximations:

• Gaussian : (Match peak and variance)

• BJK: Gaussian in

•WMAP:

• Equal variance: Np independent modes with equal variance

)log( 2 lNlll BCCZ (Bond, Jaffe & Knox)

BJK

1 2

3 3 GL L L

Approx. PDF for Band powers

22 2

ev 2 2ln ln( )

2 ( )i

S NS N

dNL

N

Fisher Information Matrix

2

:ln

iji j

Fp p

L

2

*

l1l ln ...

2

nn i

i jjp

pp

p

LL L

Expand the Likelihood L(Cl) around the best fit values

Error covariance matrix

ijji Fpp )( 1

How well are Parameters Estimated?

Eigenvalues of Inverse Fisher matrix rank order the parameter combinations (Eigenmodes).

SLOAN DIGITAL SKY SURVEY (SDSS)

0H

DM

b

tot

Mildly Perturbed universe at z=1100

Present universe at z=0

Gravitational Instability

Cosmic matter content

Standard cold dark matter

Cosmological constant + cold dark matter

Gravitational 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

Characterizing the mass distribution “power

spectrum”

Var(R) vs. R

Power spectrum of mass distribution Power spectrum of mass distribution

Sensitivity to curvatureSensitivity to curvature

Sensitivity to Dark energy fraction Sensitivity to Dark energy fraction

Sensitivity to Dark matter fractionSensitivity to Dark matter fraction

Sensitivity to Baryonic matter fractionSensitivity to Baryonic matter fraction

Cmbgg OmOlCMB

+

LSS

Weighing the NeutrinosWeighing the Neutrinos

(MacTavish et al. astro-ph/0507503)

m < 0.16 eV

3- degenerate mass

= 3 m /(94.0 eV)

f= /DM

m < 0.4 eV

m < 1.0 eV

(95% CL)

Cosmological constraints on mass

Baryonic

matter

Dark matter

Expansion rate

Dark energy

Cosmic age

Multi-parameter (7-11) joint estimation (complex covariance, degeneracies, priors,… marginal distributions) Strategies to search & Locate best parameters: Markov Chain Monte Carlo

Cosmological Parameters

Optical depth

Fig.:R.Sinha, TS

NASA/WMAP science team

Total energy density

Baryonic matter density

Dawn of Precision cosmology !!

Dark energy density

Good old Cosmology, … New trend !