Cosmology with CMB anisotropy Tarun 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 T 0 =2.725 ±0.002 K. Clinching support for Hot Big Bang model
The dominant radiation component in the universe ~ 400 CMB photons per cubic cm. (D. Scott 99)
The most perfect Black-Body spectrum in nature COBE FIRAS The CMB temperature A single number characterizes the radiation content of the universe!! COBE website
COBE-FIRAS results strongly constrain any Energy input into the CMB in the not-so-early universe 60 Ghz 600 Ghz δe E ( λ = 2.5 10 500 5000µ m) 4, ARCADE 2004 10 Ghz 30Ghz (figs: Bond, 1996)
The Perturbed Isotropic Universe 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
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
Gravitational Instability Mildly Perturbed universe at z=1100 Present universe at z=0 Cosmic matter content Ω Ω Ω tot b DM Ω Λ H 0
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 Baryonic matter Expansion rate Optical depth Fig.:R.Sinha, TS
Statistics of CMB CMB Anisotropy Sky map => Spherical Harmonic decomposition T ( θ, φ ) = l a lm Y lm ( θ, φ ) l= 2 m= l Gaussian CMB anisotropy completely specified by the angular power spectrum IF Statistical isotropy * lm l ' m' l ll ' mm' a a = C δ δ (=> Correlation function C(n,n )=h T Ti is rotationally invariant)
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 C l The Angular power spectrum of CMB anisotropy is considered a powerful tool for constraining cosmological parameters.
Low multipole : Sachs-Wolfe plateau Moderate multipole : Acoustic Doppler peaks High multipole : Damping tail CMB physics is very well understood!!!
Sensitive to curvature 1 Ω K l = 220 Fig:Hu & Dodelson 2002 l
Fig:Hu & Dodelson 2002 Sensitive to Baryon density T = 74µK
Post-COBE Ground & Balloon Experiments Python-V 1999, 2003 Boomerang 1998 DASI 2002 (Degree Angular scale Interferometer) Archeops 2002
Highlights of CMB Anisotropy Measurements (1992-2002)
NASA Launched July 2001 Wilkinson Microwave Anisotropy Probe First year data results announced on Feb. 11, 2003!
30% sky daily, Whole sky every 6 months
10 independent Difference assemblies over 5 frequencies K band 23 GHz (1 DA) Ka band 33 GHz (1 DA) CMB anisotropy signal W band 94 GHz (4 DA) Q band 41 GHz (2 DA) NASA/WMAP science team V band 61 GHz (2 DA)
dus saal baad.
NASA/WMAP science team Signal / Noise > 1for 650 Cosmic variance limited errors for 350
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 IIT Kanpur + IUCAA Black: IITK+IUCAA Red : WMAP team Saha, Jain,Souradeep 2005 (astro-ph/0508383)
Controlling other Systematics Eg.,Non-circular beam effect in CMB measurements WMAP Q beam Eccentricity =0.7 (S. Mitra, A. Sengupta, Souradeep, PRD 2004) Close to the corrections expected in the WMAP 2 nd data release
(74.4±0.3, 220.8±0.8) (74.7 ±0.5, 220.1 ±0.8) Saha, Jain,Souradeep 2005 (astro-ph/0508383) (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)
Power spectrum of mass distribution ( Tegmark et al. 2004)
CMB + (Fig: Tegmark) LSS (WMAP+SDSS analysis: Tegmark et al. 2004)
Near future : High resolution C l (SPT) CMB Task force report 2005
Gravitational Instability Mildly Perturbed universe at z=1100 Present universe at z=0 Cosmic matter content Ω Ω Ω tot b DM Ω Λ H 0
Present distribution of matter Few Gpc. SLOAN DIGITAL SKY SURVEY (SDSS)
One little telltale bump!! ξ() r = δρ( r) δρ( r ) 1 2 A small excess in correlation at 150 Mpc.! SDSS survey (astro-ph/0501171) (Einsentein et al. 2005) 150 Mpc.
Acoustic Baryon oscillations!! 150 Mpc. (Einsentein et al. 2005)
Acoustic Baryon oscillations in the matter correlation function!! 2-point correlation of density contrast 105 h -1 150 Strong evidence of Gravitational instability mechanism for structure formation (from adiabatic initial perturbations)!!! 150 Mpc. The same CMB oscillations at low redshifts!!! SDSS survey (astro-ph/0501171) (Einsentein et al. 2005)
Quantum fluctuations PARAMETERS OF THE INITIAL super adiabatic CONDITIONS amplified by FROM inflation EARLY (rapid expansion) UNIVERSE Galaxy COSMOLOGICAL & Large scale Structure PARAMETERS formation Via gravitational instability Early Universe The Cosmic screen Present Universe
The nature of initial/primordial perturbations 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 Underlying statistics Isocurvature -- no curvature fluctuations Gaussian Non-Gaussian
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 (C l TT +.. ): two polarization modes (C l EE, C l BB ) cross correlation with temperature anisotropy C l TE. (Fig:Hu & White, 97) 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.
C l TT First detection by DASI (2002) l =220-400 C l EE C l TE Regularly updated Sept 2004: CBI, DASI,CAPMAP July 2005: Boomerang
Proof of inflation? Anti-correlation peak = 137 ± 9, T = 35µK z reion 10 = 20 + 9 Adiabatic IC TE peak out of phase = 300 NASA/WMAP science team Consistent with T for 20
(MacTavish et al. astro-ph/0507503) Out of phase location of peaks Null in BB: EE, Awaiting TE relative direct to TT signature impliesof tensor perturbations, adiabatic initial a.k.a. perturbations!!! 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)
The curvature (density) of the Universe (MacTavish et al. astro-ph/0507503) Ω K =-0.037±0.04 Ω K =-0.027±0.016 Ω K =-0.022±0.017
Cosmological constraints on ν mass (MacTavish et al. astro-ph/0507503) 3-ν degenerate mass Ω ν = 3 m ν /(94.0 ev) f ν = Ω ν /Ω DM m ν m ν m ν (95% CL) < 1.0 ev < 0.4 ev < 0.16 ev
The nature of dark energy (MacTavish et al. astro-ph/0507503) Constant equation of state, w w=-0.86±0.4 w=-0.94±0.1
(MacTavish et al. astro-ph/0507503) Tensor to scalar ratio is a crucial discriminant of EU scenarios Tensor to scalar ratio A T /A S < 0.71 A T /A S < 0.36
CMB Task force report 2005
CMB Task force report 2005
Courtesy: A. Coorey (EPIC) 10-3 : reasonable low end of inflationary possibilities
PARAMETERS OF THE INITIAL CONDITIONS FROM EARLY UNIVERSE COSMOLOGICAL PARAMETERS Early Universe The Cosmic screen Present Universe
CMB anisotropy has two independent aspects: C l dk = Pk ( ) G ( k) k P( k) Primordial power spectrum from Early universe G( k) Post recombination Radiation transport in a given cosmology (Tegmark & Zaldariagga 97, Gawaiser & Silk 00, Matsumiya et al. 02..) l
Suppression of power on low multipoles (l=2,3) NASA/WMAP science team Low Quadrupole T 2 = 8 ± 2 µ K (COBE T 10 7 2 = + 4 µ K ) = 2
Recovering the primordial power spectrum (Shafieloo & Souradeep, 2004 PRD ) Primordial power spectrum from Early universe can deconvolved from CMB anisotropyspectrum Horizon scale C l = dk k P( k) G ( k) l Improved Error sensitive iterative Richardson-Lucy deconvolution method Recovered spectrum shows an infra-red cut-off on Horizon scale!!! Is it cosmic topology? Signature of pre-inflationary phase? New physics?.
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 A reconfirmation of our results using different deconvolution method! (Tocchini-Vaentini, Hoffman, Silk astro-ph/0509478)
Two independent aspects of CMB anisotropy : C C C C PS( k), PT( k), Piso( k) TT EE BB TE Primordial power spectra from Early universe = = = = dk k dk k dk k dk k Pk ( ) Pk ( ) P( k) G G G TT EE BB ( k) ( k) ( k) TE Pk ( ) G ( k) TT EE BB TE G ( k), G ( k), G ( k), G ( k) Post recombination Radiative transport kernels in a given cosmology
Absence of large scale power Intriguing lack of correlations at large angular scales (θ 60 ) Can imply more than just the suppression of power in the low multipoles! NASA/WMAP science team
Asymmetries in the CMB anisotropy 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?).. WMAP first year data Bianchi template Difference map Broadly, statistical properties are not invariant under rotations I.e., Breakdown of Statistical Isotropy? Low N-S asymmetry High N-S asymmetry Fig: H. K. Eriksen, et al. 2003
Statistics of CMB Possibilities: Cn ( ˆ, nˆ ) Cn ( ˆ nˆ ) 1 2 1 2 Statistically Isotropic, Gaussian models Statistically Isotropic, non-gaussian models Statistically An-isotropic, Gaussian models Statistically An-isotropic, non-gaussian models * lm l ' m' l ll ' mm' a a C δ δ
Sources 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
Figs. J. Levin Cn ( ˆ, nˆ ) Cn ( ˆ nˆ ) 1 2 1 2 Beautiful Correlation patterns could underlie the CMB tapestry Can we measure correlation patterns? the COSMIC CATCH is
Bipolar Power spectrum (BiPS( BiPS) ) : A Generic Measure of Statistical Anisotropy 1 Recall: C( nˆ ˆ ) ( ˆ, ˆ 1 n2 = dr C Rn1 Rn2) 2 8π Bipolar multipole index κ 1 = 8π dω dω ( ) ( 2 1, 2 1 2 dr χ n n R C Rn Rn ˆ ˆ ) 2 A weighted average of the correlation function over all rotations Hajian & Souradeep ApJ. Lett 2003 Hajian, Souradeep & Cornish ApJ. Lett. 2005 χ ( R ) = ( R ) m = D mm Characteristic Wigner function rotation matrix
Statistical Isotropy κ = κ 0 δ 0 Correlation is invariant under rotations C ( Rnˆ, ˆ ) ( ˆ, ˆ 1 Rn2 = C n1 n2) κ 2 1 = ( 2 + 1) dω 2 8π 2 ( ˆ ˆ n dω C n1, n2)[ drχ ( R 1 n 2 )] 2 dr ( ) δ 0 χ R =
BiPS: : In Harmonic Space Correlation is a two point function on a sphere C LM ( n1, n2) Al l { Yl ( n ) Yl ( n 1 2 1 1 2 2 l l LM Inverse-transform A LM l l 1 2 = = 1 2 dω n 1 dω n 2 C( n { Y = l 1 ( n1 ) Y LM C m m 1 2 l l 1 2 )} m m 1 l LM 2 2 ( n Y 1 2 l m 1 )} ( n LM 1 ) Y n Yl n Yl n * 1, 2){ ( 1) ( 2)} LM 1 Clebsch-Gordan 2 BiPoSH Bipolar spherical harmonics. l 2 m 2 ( n 2 ) = m m 1 2 a l m 1 1 a l 2 m 2 CLM l 1m12 l m2 Linear combination of off-diagonal elements
Recall: Coupling of angular momentum states l m l m M l l l + m + m + M 1 1 2 2 1 2 1, 1 2 = 0 BiPoSH coefficients : A M l l 1 2 = a a * l1m 1 l2 M + m m 1 1 M C l 1m1 l2 M + m1 Complete,Independent linear combinations of off-diagonal correlations. Encompasses other specific measures of off-diagonal terms, such as D a - Durrer et al. l 98 : lm a l + 2 m = - Prunet et al. 04 : ( i) M M D a a + + = A C + + l lm M M A C ll ' l + 2 M l 1 m i M m ll' l m l 1 m i l m BiPS: rotationally invariant κ M, l 1, l 2 A M l l 1 2 2 0
SI violation : a lm a * l ' m ' C l δ ll' δ mm' Radical breakdown a l ' m ' a a lm a * l ' m ' * l ' m ' a lm a * lm (Bond, Pogosyan & Souradeep 1998, 2002)
SI violation: a a C δ δ * lm l ' m' l ll ' mm' Understanding BiPoSH coefficients A 4 M ll ' LM A ll ' = almalm' C mm' LM lml ' m ' Measure cross correlation in a lm A 2 M ll '
Spherical harmonics alm Spherical Harmonic coefficents C l Angular power spectrum Bipolar spherical harmonics M A ll' BiPoSH coefficents κ BiPS Bipolar Power spectrum (BiPS( BiPS) ) : A Generic Measure of Statistical Anisotropy
Spherical harmonics Spherical Harmonic Transforms C l alm Angular power spectrum Bipolar spherical harmonics M A ll' BipoSH Transforms κ BiPS (Bipolar Power Spectrum) Bipolar Power spectrum (BiPS( BiPS) ) : A Generic Measure of Statistical Anisotropy
Orientation independent. Measure of Statistical Isotropy A κ M ll' = = ll' M Stat.isotropy mm' A a M ll' lm κ 2 a l' m' = B κ 0 C δ M lml ' m' 0 SH transform of the map bias 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 )
Statistical Isotropy of CMB Anisotropy WMAP CMB anisotropy map Fig: NASA/WMAP science team Hajian & Souradeep ApJ. Lett 2003 Hajian, Souradeep & Cornish ApJ. Lett. 2005 WMAP Angular power spectrum Fig: NASA/WMAP science team W(l) WMAP Bipolar power spectrum BiPS imply (BiPS) WMAP 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 C l adequate descriptor of CMB? (Detection of cosmic topology? Is the universe observably finite?)
Thank you!!! CMB Task force report 2005