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Cosmology with CMB anisotropy. Tarun Souradeep. I.U.C.A.A, Pune. WHEPP-9 (Jan 10, 2005). The Isotropic Universe . Cosmic Microwave Background. - PowerPoint PPT Presentation
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Cosmology Cosmology with CMB with CMB
anisotropyanisotropyTarun Souradeep
I.U.C.A.A, Pune
WHEPP-9 (Jan 10, 2005)
The Isotropic Universe
Serendipitous discovery of the dominant Radiation content of the universe as an extremely isotropic, Black-body bath at temperature
TT00=2.725=2.725§§0.0020.002K .K .
““Clinching support for Hot Big Bang model”Clinching support for Hot Big Bang model”
The dominant radiation component in the universe
(D. Scott ’99)
~ 400 CMB photons per cubic cm.
The most perfect Black-Body spectrum in nature
COBE website
COBE –FIRAS
The CMB temperature –A single number
characterizes the radiation content of the universe!!
(figs: Bond, 1996)
COBE-FIRAS results strongly constrain any Energy input into the CMB in the not-so-early universe
)5000500(
4 ,105.2m
EE
10 Ghz30Ghz
60 Ghz 600 Ghz
ARCADE 2004
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
The Perturbed Universe The Isotropic Universe
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
0H
DM
b
tot
Mildly Perturbed universe at z=1100
Present universe at z=0
Gravitational Instability
Cosmic matter content
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
),(),(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 theangular 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 !!!
Fig:Hu & Dodelson 2002
Sensitive to curvature
K1220l
l
Fig:Hu & Dodelson 2002
Sensitive to Baryon density
KT 74
Boomerang 1998
DASI 2002 (Degree Angular scale
Interferometer) Archeops 2002
Python-V 1999, 2003
Post-COBE Ground & Balloon Experiments
Highlights of CMB Anisotropy Measurements (1992- 2002)
First year data results announced on Feb. 11,
2003 !
NASA Launched July 2001
Wilkinson Microwave Anisotropy Probe
30% sky daily, Whole sky every 6 months
NASA/WMAP science team
K band 23 GHz (1 DA)
Ka band 33 GHz (1 DA)
Q band 41 GHz (2 DA)
V band 61 GHz (2 DA)
W band 94 GHz (4 DA)
CMB anisotropy signal
10 independent Difference assemblies over 5 frequencies
dus saal baad ….
NASA/WMAP science team
650for 1 Noise / Signal
350for errors limited varianceCosmic
IIT Kanpur + IUCAA
Saha, Jain,Souradeep 2005(astro-ph/0508383)
Independent, self contained analysis of WMAP multi-frequency maps Only input : CMB anisotropy is achromatic (frequency independent)No extraneous foreground info. ! I.e., free of uncertainty of foreground modeling
Black: IITK+IUCAA
Red : WMAP team
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 expected in
the WMAP 2nd data release
(74.40.3, 220.80.8)(74.7 0.5, 220.1 0.8)
(49.6 1.2, 545 17)(48.8 0.9, 546 10)
(42.2 0.9, 418.7 5.5) (41.0 0.5, 411.7 3.5)
Saha, Jain,Souradeep 2005(astro-ph/0508383)
Power spectrum of mass distribution
( Tegmark et al. 2004)
(Fig: Tegmark)CMB+LSS
(WMAP+SDSS analysis: Tegmark et al. 2004)
CMB Task force report 2005
Near future : High resolution Cl (SPT)
0H
DM
b
tot
Mildly Perturbed universe at z=1100
Present universe at z=0
Gravitational Instability
Cosmic matter content
SLOAN DIGITAL SKY SURVEY (SDSS)
Few Gpc.
Present distribution of matter
One little telltale bump !! A small excess in correlation at 150
Mpc.!SDSS survey
(astro-ph/0501171)
150 Mpc.
(Einsentein et al. 2005)
1 2( ) ( ) ( )r r r
Acoustic Baryon oscillations!!
150 Mpc.
(Einsentein et al. 2005)
2-po
int c
o rre
latio
n of
de
nsi ty
con
tra s
t Acoustic Baryon oscillations in the matter
correlation function !!
The same CMB oscillations at
low redshifts !!!SDSS survey
(astro-ph/0501171)
Strong evidence ofGravitational instability mechanism
for structure formation (from adiabatic initial perturbations) !!!
150 Mpc.
(Einsentein et al. 2005)
105 h-1 ¼ 150
Quantum fluctuations
super adiabatic amplified by
inflation (rapid expansion)
Galaxy & Large scale
Structure formation
Via gravitational instability
Early Universe
Present Universe
The Cosmic screen
PARAMETERS OF THE
INITIAL CONDITIONS
FROM EARLY UNIVERSE
COSMOLOGICAL
PARAMETERS
Power spectrum‘Nearly’ Scale invariant /scale free form
( for the Geometry & Topology of the universe)
Spin characteristics Scalar --- Density perturbations
Tensor --- Gravity waves
Vector --- rotational modes Type of scalar perturbations
Adiabatic --- no entropy fluctuations
Isocurvature -- no curvature fluctuations
Underlying statistics Gaussian
Non-Gaussian
The nature of initial/primordial perturbations
Thompson scattering of the CMB anisotropy quadrupole at the surface of last scattering generates a linear polarization pattern in the CMB.
Three additional Power spectra (ClTT +.. ):
• two polarization modes (ClEE , Cl
BB )
• cross correlation with temperature anisotropy ClTE .
Initial metric perturbation mix correspondence :
Scalar perturbations predominantly generate the Electric (E) polarization mode.
Vector perturbations predominantly generate the magnetic (B) polarization mode .
Tensor perturbations generate the both modes in comparable amounts . Temperature anisotropy Cross-correlation only with the E-mode.
(Fig:Hu & White , 97)
First detection by DASI (2002)
l =220-400
Regularly updated Sept 2004: CBI, DASI,CAPMAP
July 2005: Boomerang
ClEE
ClTE
ClTT
NASA/WMAP science team
Proof of inflation?Anti-correlation peak
KT 35,9137
10920
reionz
20for with Consistent T
Adiabatic ICTE peak out of
phase 300
(MacTavish et al. astro-ph/0507503)
Out of phase location of peaks in EE, TE relative to TT implies adiabatic initial perturbations!!!
Null BB: Awaiting direct signature of tensor perturbations, a.k.a. gravity waves !!!
(MacTavish et al. astro-ph/0507503)
BUT, please read the fine print !Data combos, priors, parameterization
BUT, please read the fine print !Data combos, priors, parameterization,…
(MacTavish et al. astro-ph/0507503)
(MacTavish et al. astro-ph/0507503)
K=-0.037§0.04
The curvature (density) of the Universe
K=-0.027§0.016K=-0.022§0.017
(MacTavish et al. astro-ph/0507503)
m < 0.16 eV
3- degenerate mass
= 3 m /(94.0 eV)
f= /DM
m < 0.4 eVm < 1.0 eV
(95% CL)
Cosmological constraints on mass
(MacTavish et al. astro-ph/0507503)
w=-0.94§0.1
w=-0.86§0.4
Constant equation of state,
w
The nature of dark energy
(MacTavish et al. astro-ph/0507503)
AT/AS < 0.71
AT/AS < 0.36
Tensor to scalar ratio
Tensor to scalar ratio is a crucial discriminant of EU scenarios
CMB Task force report 2005
CMB Task force report 2005
Courtesy: A. Coorey (EPIC)
10-3 : reasonable low end of inflationary
possibilities
Early Universe
Present Universe
The Cosmic screen
PARAMETERS OF THE
INITIAL CONDITIONS
FROM EARLY UNIVERSE
COSMOLOGICAL
PARAMETERS
CMB anisotropy has two independent aspects:
( ) ( )l P kdkC Gk
k
( )P k ( )lG kPost recombination Radiation transport in a given cosmology
Primordial power spectrum from Early universe
(Tegmark & Zaldariagga 97, Gawaiser & Silk ’00, Matsumiya et al. ’02..)
NASA/WMAP science team
)74102 (COBE
2 282 Quadrupole Low
KT
KT
Suppression of power on low multipoles (l=2,3)
(Shafieloo & Souradeep, 2004 PRD )
Improved Error sensitive iterative Richardson-Lucy deconvolution method
)()( kGkPk
dkC ll
Primordial power spectrum from Early universe can deconvolved from CMB anisotropyspectrum
Recovered spectrum shows an infra-red cut-off on Horizon scale !!! Is it cosmic topology ? Signature of pre-inflationary phase ? New physics ? ….
Recovering the primordial power spectrum
Horizon scale
0.68
0.71
0.75
0.040
0.044
0.048
0.31
0.27
0.23
Wavelet Decomposition of features(TS+ Rangarajan, Panigrahi, Manimaran: in progress)
Infrared cutoff
Superimposed Oscillations
Recovery of the primordial power spectrum
(Tocchini-Vaentini, Hoffman, Silk astro-ph/0509478)
A reconfirmation of our results using different deconvolution method !
Two independent aspects of CMB anisotropy :
( )
( )
( )
( )
( )
( )
( ) ( )
TT TT
EE
B
EE
B B
T
B
ETE
dkCkdkCk
dkC
G k
G k
G k
P k
P k
P
G k
k
P k
kdkCk
( ), ( ), ( )S T isoP k P k P k ( ), ( ), ( ), ( )TT EE BB TEG k G k G k G k
Primordial power spectra from Early universe
Post recombination Radiative transport kernels in a given cosmology
Absence of large scale power
NASA/WMAP science team
Intriguing lack of correlations at large angular scales ( ¸ 60±)
Can imply more than just
the suppression of power in the
low multipoles !
Asymmetries in the CMB anisotropy
Broadly, statistical properties are not invariant under rotations
I.e., Breakdown of Statistical Isotropy ?
N-S asymmetry Eriksen, et al. 2004, Hansen et al. 2004 (in local power)Larson & Wandelt 2004, Park 2004 (genus stat.)
Special directions “Axis of Evil”Tegmark et al. 2004 (l=2,3 aligned)Copi et al. 2004 (multipole vectors)Land & Magueijo 2004 (cubic anomalies)Prunet et al., 2004 (mode coupling)
Underlying `template’ pattern Jaffe et al. 2005 (Bianchi VIIh:mild cosmic rotation?)..
High N-S asymmetry
Low N-S asymmetry
Fig: H. K. Eriksen, et al. 2003
WMAP first year data
Bianchi template
Difference map
Possibilities:• Statistically Isotropic, Gaussian models• Statistically Isotropic, non-Gaussian models• Statistically An-isotropic, Gaussian models• Statistically An-isotropic, non-Gaussian models
Statistics of CMB
1 2 1 2ˆ ˆ ˆ ˆ( , ) ( )C n n C n n
*' ' ' 'lm l m l ll mma a C
Sources of Statistical AnisotropySources of Statistical Anisotropy• Ultra large scale structure and cosmic topology.
• Anisotropic cosmology• Primordial magnetic fields (based on Durrer et al. 98, Chen et al. 04)
• Observational artifacts: – Anisotropic noise – Non-circular beam – Incomplete/unequal sky coverage – Residuals from foreground removal
Can we measure correlation patterns?the COSMIC CATCH is
Beautiful Correlation patterns could underlie the CMB tapestry Figs. J. Levin
1 2 1 2ˆ ˆ ˆ ˆ( , ) ( )C n n C n n
2
21221)ˆ,ˆ()(
81
nnCdndnd
Bipolar Power spectrum (BiPS) :Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical AnisotropyA Generic Measure of Statistical Anisotropy
A A weighted averageweighted average of the of the correlation function over all correlation function over all
rotationsrotations
)ˆ,ˆ(8
1)ˆˆ( :Recall 21221 nnCdnnC Bipolar multipole index
Wigner Wigner rotation rotation matrixmatrix
)()(
mmmD
Characteristic Characteristic functionfunction
Hajian & Souradeep ApJ. Lett 2003
Hajian, Souradeep & Cornish ApJ. Lett. 2005
2
22122
)](8
1[)ˆ,ˆ()12(21
dnnCdd nn
0)(
d
Statistical IsotropyStatistical Isotropy
Correlation is invariant under rotations
)ˆ,ˆ()ˆ,ˆ( 2121 nnCnnC
00
• Correlation is a two point function on a sphere
• Inverse-transform )()(
)}()({21
21
2211
21
2121
21
nYnYCnYnY
mlmlmm
LMmmll
LMll
LMllLMll
LMll nYnYAnnC )}()({),( 2121 21
21
21
LM
mmmlml
LMllnnLMll
mlmlCaa
nYnYnnCddA
221121
2211
212121*
2121 )}()(){,(
BiPS: In Harmonic SpaceBiPS: In Harmonic Space
BiPoSH
Linear combination of off-diagonal elements
Bipolar spherical harmonics.
Clebsch-Gordan
0||21
21,,
2 llM
MllABiPS:BiPS:
rotationally invariantrotationally invariant
M
mmMlml
Mll mMlml
CaaA
12111
121121
* BiPoSH BiPoSH
coefficients :coefficients :• Complete,Independent linear combinations of off-diagonal correlations.• Encompasses other specific measures of off-diagonal terms, such as
- Durrer et al. ’98 :- Prunet et al. ’04 :
M
Mmliml
Mllimllm
il CAaaD
1'1
)(
M
Mmlml
Mllmllml CAaaD
2'2
Recall: Coupling of angular momentum states Mmlml |2211 0, 21121 Mmmlll
''*
'' : violationSI mmlllmllm Caa
Radical breakdown
**''''
*''
lmlmmlml
mllm
aaaa
aa
(Bond, Pogosyan & Souradeep 1998, 2002)
MllA2
'
MllA4
'
Understanding BiPoSH coefficients
*' ' ' '
SI violation
:
lm l m l ll mma a C
' '''
'
Measure cross correlation in
lml m
LMlm lm
mm
LM
lm
ll a a CA
a
Bipolar spherical harmonics
Spherical Harmonic coefficents
BiPoSH coefficents
Angular power spectrum
BiPS
lma MllA
'
lC
Spherical harmonics
Bipolar Power spectrum (BiPS) :Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical AnisotropyA Generic Measure of Statistical Anisotropy
Bipolar spherical harmonics
Spherical Harmonic Transforms
BipoSH Transforms
Angular power spectrum
BiPS(Bipolar Power
Spectrum)
lma MllA
'
lC
Spherical harmonics
Bipolar Power spectrum (BiPS) :Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical AnisotropyA Generic Measure of Statistical Anisotropy
Measure of Statistical IsotropyMeasure of Statistical Isotropy
00
isotropy Stat.
2
''
'''
' ''
BA
CaaA
Mll
Mll
Mmllm
mm
Mll mlml
• Averaging over l,l’& M beats down Cosmic variance .• Fast: Advantage of fast SH transform. (1 min. /alpha 1.25 GHz proc.: Healpix 512, BiPS upto 20 )
• Orientation independent.
bias
SH transform of the map
Statistical Isotropy of CMB Statistical Isotropy of CMB AnisotropyAnisotropy
W(l)
WMAP CMB anisotropy map
WMAP Angular power spectrum
WMAP Bipolar power spectrum (BiPS)
Fig: NASA/WMAP science team
Fig: NASA/WMAP science team
Hajian & Souradeep ApJ. Lett 2003
Hajian, Souradeep & Cornish ApJ. Lett. 2005
BiPS implyWMAP is Statistically
Isotropic !!
Cosmology with CMB anisotropy• Precise values of the parameters of the ‘working model’ of
cosmology.
• Direct evidence of gravitational instability being responsible for structure formation.
• Initial/primordial perturbations from (simple) inflation– adiabatic density perturbations – Gaussian random fields – A non-zero tensor component ? (cosmic gravity wave background )
• Observable signatures of Ultra-large structure of the cosmos, or, new physics in early universe– infra-red cutoff & feature in the primordial power spectrum – Violation of statistical isotropy : Are Cl adequate descriptor of CMB ?
(Detection of cosmic topology ? Is the universe observably finite ?)
Thank Thank you !!!you !!!
CMB Task force report 2005
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