Tarun Souradeep
description
Transcript of Tarun Souradeep
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 !