CMB anisotropy. Tarun Souradeep. ICSW-07 IPM, Tehran (Jun 2-9, 2007) I.U.C.A.A, Pune, India

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1 CMB anisotropy ICSW-07 IPM, Tehran (Jun 2-9, 2007) Tarun Souradeep I.U.C.A.A, Pune, India

2 Cosmic Microwave Background X R H /33

3 Cosmic Super IMAX theater 0.5 Myr Here & Now (14 Gyr) 14 GPc Transparent universe Causal horizon c s τ rec Opaque universe

4 Dissected CMB Angular power spectrum Low multipole : Sachs-Wolfe plateau Moderate multipole : Acoustic Doppler peaks High multipole : Damping tail CMB physics is very well understood!!!

5 Music of the Cosmic Drum

6 Ping the Cosmic drum (Fig: Einsentein ) More technically, the Green function

7 Ripples in the different constituents 150 Mpc. (Einsentein et al. 2005)

8 Perturbed universe: superposition of random `pings (Fig: Einsentein )

9 CMB Angular power spectrum Sensitive to curvature 1 Ω K l = 220 Fig:Hu & Dodelson 2002 l

10 Fig:Hu & Dodelson 2002 CMB Angular power spectrum Sensitive to Baryon density ΔT = 74μK

12 Estimating the Angular power spectrum (Souradeep 1998)

13 Estimating the Angular power spectrum Cosmic Variance of the unbiased estimator Homo., Uncorrelated noise: Inevitable error for one sky Gaussian beam : var ( ~ ) C B 2 = + l l crude account of incomplete sky ( 2l + 1) f θ sky C N l = [ C S σ 2 exp( l 2 2) ] 2 N 4π N pix σ 2 pix σ 2 ( θ ) = exp, = exp 2σ 2 θ, σθ = θfwhm 2σ 2 Bl l θ 2 8ln 2 1 σθ 2 N 1 Noise term dominates beyond beam width

14 Post-COBE Ground & Balloon Experiments Python-V 1999, 2003 Boomerang 1998 DASI 2002 (Degree Angular scale Interferometer) Archeops 2002

15 Highlights of CMB Anisotropy Measurements ( )

16 First NASA CMB Satellite mission 2003 Second NASA CMB Satellite mission

17 Wilkinson Microwave Anisotropy Probe NASA : Launched July 2001 WMAP: WMAP: 3-1- year year results results announced announced on on Mar, Feb, !! NASA/WMAP science team

18 30% sky daily, Whole sky every 6 months

19 WMAP map of CMB anisotropy CMB temperature T cmb = K -200 μ K < Δ T < 200 μ K Δ T rms ¼70μ K

21 WMAP-3yr: Angular power spectrum NASA/WMAP science team

22 WMAP multi-frequency maps K band 23 GHz Ka band 33 GHz CMB anisotropy signal W band 94 GHz Q band 41 GHz V band 61 GHz

23 CMB anisotropy signal is frequency independent Image courtesy WMAP homepage

24 Cosmic Microwave Background 60 Ghz 600 Ghz (fig: Bond, 1996) 10 GHz 30 GHz ARCADE Ghz 30Ghz future: 3-90 GHz

25 WMAP: Angular power spectrum Independent, self contained analysis of WMAP multi-frequency maps IIT Kanpur + IUCAA Saha, Jain, Souradeep (WMAP1: Apj Lett 2006) WMAP 2 nd release : Eriksen et al. ApJ (5 international groups)

26 Peaks of the angular power spectrum (74.1±0.3, 219.8±0.8) (74.7 ±0.5, ±0.8 (48.3 ±1.2, 544 ±17) (48.8 ±0.9, 546 ±10) (41.7 ±1.0, ±5.6) (41.0 ± 0.5, ±3.5) (Saha, Jain, Souradeep Apj Lett 2006)

Two polarization modes E&B Four CMB spectra : C l TT, C l EE,C l BB,C l TE Density (scalar) perturbations

27 CMB Polarization Thompson scattering at redshift z=1100 (surface of last scattering) generates a linear polarization pattern in the CMB sky. Two polarization modes E&B Four CMB spectra : C l TT, C l EE,C l BB,C l TE Density (scalar) perturbations generate only E mode polarization. E-mode ¼ μ K Gravitational waves generate both the modes in comparable amounts. B-mode ¼ μ K B-mode measures cosmic gravity wave background.

28 CMB Polarization Thompson scattering of the CMB anisotropy quadrupole at the surface of last scattering generates a linear polarization pattern in the CMB. (Fig:Hu & White, 97)

29 E modes (Gradient) B modes (Curl)

30 (Boomerang 2003, WMAP-3) Current status of CMB Spectra Null BB: Awaiting direct signature of tensor perturbations, a.k.a. Out of phase location of peaks in EE, TE relative to TT implies adiabatic initial perturbations!!! cosmic gravity waves!!! Proof of inflation!

31 WMAP map of CMB Polarization NASA/WMAP science team 2006

32 WMAP-3yr: Angular power spectra NASA/WMAP science team

33 WMAP CMB Polarization challenge (ongoing: Rajib Saha, Simon Prunet, P. Jain,TS)

34 CMB Task force report 2005

35 CMB Task force report 2005

36 WMAP-1yr Timeline of CMB experiments now WMAP-3yr WMAP-8yr Planck (ESA) Next Gen. space CMBPOL CMB Task force report 2005

37 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

38 Present distribution of matter Few Gpc. SLOAN DIGITAL SKY SURVEY (SDSS)

39 One little telltale bump!! r r ξ() r = δρ( ) δρ( ) 1 2 A small excess in correlation at 150 Mpc.! SDSS survey (astro-ph/ ) (Einsentein et al. 2005) 150 Mpc.

40 Acoustic Baryon oscillations in the matter correlation function!! 2-point correlation of density contrast 105 h -1 ¼ 150 Undeniable proof of Gravitational instability mechanism for structure formation (from adiabatic initial perturbations)!!! 150 Mpc. The same CMB oscillations at low redshifts!!! SDSS survey (astro-ph/ ) (Einsentein et al. 2005)

41 Ripples in the different constituents

43 Quantum fluctuations super adiabatic amplified by inflation (rapid expansion) Galaxy & Large scale Structure formation Via gravitational instability Early Universe The Cosmic screen Present Universe Who pinged the Cosmic drum?

44 Generic Inflation model A scalar field displaced from the minima of its potential Linde s chaotic inflation && φ + 3 Hφ& + V = 0 3 ρ φ& 1 2 H 2 = = 2 +V p = 1 φ & 2 V 2

45 Generic Inflation model A scalar field displaced from the minima of its potential Deceleration = 3 2 : q = a&& ah ( ρ + 3 p) ( & φ 2 V ) = 3 ρ ρ 2 Inflation φ & 2 / V < 1

46 Generation of fluctuations " DeSitter" q.fluc.: δφ δφ ( ) H No. of e - folds : N = H dt δn = Hδt e = H & φ δφ

47 ln 4 ln 2 1 ln ln parameters roll Slow φ π δ ε φ φ φ δ φ π φ ε d H d m a d d H d H d m H P P = + = = & & && & (Souradeep, Thesis 1995)

48 [ ] [ ] ln 4 3) )( (, 0 ) ( 0 ) (, φ π δ ε δ δ ε η η δφ d H d m H H m a a V H m a a V v V k v u V k u ah v a u P eff T eff S k T k k S k k k k k = = = = + = + & & Scalar & Tensor perturbations (Fig:Souradeep, Thesis 1995)

49 Early Universe in CMB The Background universe Homogeneous & isotropic space: Cosmological principle Flat (Euclidean) Geometry The nature of initial/primordial perturbations Power spectrum : Nearly Scale invariant /scale free form Spin characteristics: (Scalar) Density perturbations cosmic (Tensor) Gravity waves? Type of scalar perturbation: Adiabatic -- no entropy fluctuations Underlying statistics: Gaussian but global topology? but are there features?

50 Detecting the relic GW background : Energy scale & mechanism of inflation

51 Early Universe in CMB Tensor to scalar ratio is crucial discriminant of EU scenarios Scalar --- Density perturbations Large scale structure in galaxy clustering Tensor --- Gravitational waves Relic stochastic GW background Vector --- rotational modes Perhaps unimportant, but primordial magnetic field COBE Tensor to scalar ratio in the CMB WMAP WMAP+SDSS (Souradeep & Sahni, 1992, Souradeep, Ph.D.thesis, 1995)

52 Courtesy: A. Coorey (EPIC) 10-3 : reasonable low end of inflationary possibilities

53 Cosmic Gravity wave background First CMB (COBE) normalized GW spectrum Souradeep & Sahni 1992 Spectral Energy Density Amplitude sets the energy scale of Inflation CMB Task force report 2005

54 Measuring the primordial power spectrum: Features as signatures of new physics

55 Primordial Power spectrum? CMB anisotropy has two independent aspects: C l dk = Pk ( ) G ( k) l k P( k) Primordial power spectrum from Early universe G( k) l Post recombination Radiation transport in a given cosmology

56 Primordial power spectrum from WMAP Horizon scale (Shafieloo & Souradeep, 2004 PRD ) (Shafieloo & Souradeep, ongoing for WMAP-3 ) C l = dk k P( k) G ( k) Improved Richardson-Lucy deconvolution method (Error sensitive) Recovered spectrum shows an infra-red cut-off on Horizon scale!!! Is it QG physics? cosmic topology? Signature of pre-inflationary phase? String cosmology?. l

57 Primordial Power spectrum? The Grand program : C C C C PS( k), PT( k), Piso( k) TT l EE l BB l TE l Primordial power spectra from Early universe = = = = dk k dk k dk k dk k Pk ( ) Pk ( ) P( k) G G G TT l EE l BB l ( k) ( k) ( k) TE Pk ( ) G ( k) l TT EE BB TE Gl ( k), Gl ( k), Gl ( k), Gl ( k) Post recombination Radiative transport kernels in a given cosmology

58 Beyond C l : Measuring correlation patterns in CMB Bipolar Sph. Harmonic rep. (BiPS: Bipolar power spectra)

North-South asymmetry Eriksen, et al. 2004,2006; Hansen et al. 2004 (in local power) Larson & Wandelt 2004, Park 2004 (genus stat.).. Special directions ( Axis of Evil ) Tegmark et al.

59 North-South asymmetry Eriksen, et al. 2004,2006; Hansen et al (in local power) Larson & Wandelt 2004, Park 2004 (genus stat.).. Special directions ( Axis of Evil ) Tegmark et al (l=2,3 aligned), 2006 Copi et al (multipole vectors),,2006 Land & Magueijo 2004 (cubic anomalies), Prunet et al., 2004 (mode coupling) Bernui et al (separation histogram) Wiaux et al Anomalies in the WMAP CMB maps Underlying patterns T.Jaffe et al. 2005, Statistical properties are not Cosmic topology (Poincare Dodecahedron) Anisotropic, rotating cosmos (Bianchi VIIh) invariant under rotation of the sky Breakdown of statistical isotropy (cosmological principle)?

60 Can we measure correlation patterns? the COSMIC CATCH is

61 Advanced Statistics of CMB Δ T(n) : smooth Gaussian random function on a sphere (sky map), i.e., Completely specified by the two-point correlation Cn ( ˆ, nˆ ) ΔTn ( ˆ ) ΔTn ( ˆ ) Statistical isotropy implies C l 2l + 1 Cn ( ˆ, n ˆ ) Cn ( ˆ n ˆ ) = P( n ˆ n ˆ ) l l 1 2 Most general, Bipolar Spherical Harmonic Expansion 12 4π is sufficient C l Cn (, n) Cn ( n) = A { Y ( n ) Y ( n )} ll LM LM ll l 1 l 2 LM

62 Recall: Coupling of angular momentum states l m l m lm l l l l + l m + m + M , 1 2 = 0 BiPoSH coefficients : A lm l l 1 2 = a a * l1m 1 l2 M + m m 1 1 lm C l 1m1 l2 M + m1 Complete,Independent linear combinations of off-diagonal correlations. BiPS: rotationally invariant l κ M, l 1, l 2 A l M l l Statistical Isotropy l κ = κ 0 δ l0

63 Spherical harmonics alm Spherical Harmonic coefficents C l Angular power spectrum Bipolar spherical harmonics A l ' M ll BiPoSH coefficents l κ BiPS Bipolar Power spectrum (BiPS( BiPS) ) : A Generic Measure of Statistical Anisotropy

64 Spherical harmonics alm Spherical Harmonic Transforms C l Angular power spectrum Bipolar spherical harmonics A l ' M ll BipoSH Transforms l κ BiPS (Bipolar Power Spectrum) Bipolar Power spectrum (BiPS( BiPS) ) : A Generic Measure of Statistical Anisotropy

65 Spherical harmonics alm Spherical Harmonic Transforms Bipolar spherical harmonics A l ' M ll BipoSH Transforms C l Angular power spectrum l κ BiPS Statistical Isotropy l 0 i.e., NO Patterns κ = κ δ l0

66 Statistical Isotropy of CMB Anisotropy Amir Hajian thesis 2006 WMAP Angular power spectrum WMAP CMB anisotropy map Fig: NASA/WMAP science team W(l) Fig: NASA/WMAP science team BiPS: : Measure of statistical isotropy BiPS: : Spectroscopy of Cosmic topology Diagnostic of systematic effects/observational artifacts in the map Differentiate Cosmic vs. Galactic B-mode B polarization WMAP Bipolar power spectrum (BiPS) BiPS Hajian & Souradeep ApJ. Lett 2003, ApJ. Lett. 2005, New Astron Rev. 2006, PRD 2006,

67 Is the Universe compact? Simple Toroidal space more complicated space

68 Simple Torus (Euclidean) BiPS Spectroscopy of!?! Cosmic topology MC spherical space Compact hyperbolic space

69 BiPS signature of a soccer ball universe (Hajian, Pogosyan, TS, Contaldi, Bond : in progress.) Ω K = Ideal, noise free maps predictions κ l l

70 BiPS signature of a soccer ball universe (Hajian, Pogosyan, TS, Contaldi, Bond : in progress.) Ω tot =1.013 κ l Ideal, noise free maps predictions l

71 BiPS signature of Flat Torus spaces κ l l Hajian & Souradeep (astro-ph/ )

72 Thank you!!! How Big is the Observable Universe? Relative to the local curvature & topological scales

73 Model free Foreground removal For each frequency channel, i : CMB anisotropy is achromatic : a = Ba + Ba + a C F n lm l lm l lm lm Linear combinations of maps of different frequency channels, i. a i= n a i = w i lm lm l i i= 1 B l C() i lm a = Such that CMB signal is untouched in the final map ) constant i = n i = 1 i w l = 1 Determine weights that minimize total power C =< a a >= [ W][ C ][ W] T * l lm lm l Foreground cleaned map: [ e ] = ( ) [ W] (Tegmark & Efstathiou 96, Tegmark 2003) l T T [ Cl ][ e] = [][ ec][] e l T

74 WMAP CMB Polarization challenge 100% 10% 1% WMAP noise (ongoing: Rajib Saha, Simon Prunet, P. Jain,TS)

75 WMAP CMB Polarization challenge (ongoing: Rajib Saha, Simon Prunet, P. Jain,TS)

76 WMAP CMB Polarization challenge (ongoing: Rajib Saha, Simon Prunet, P. Jain,TS)

77 BiPS Spectroscopy of Cosmic topology (Himan Mukhopadhyay,TS, in progress.) Symmetry requirements for even BiPS: Group-theoretic 1. 2n-fold symmetry There should exist at least one plane characterized by such that R nˆ ( πγ ) = γr ( π) " γî Γ nˆ ˆn 2. Symmetry under reflection x r x r Let and be images of each other for the same plane. Then { d( x r, γx r )} º { d( x r, γx r )} " γî Γ

78 Which spaces satisfy 1 &2? Flat compact spaces Single-action spherical compact spaces r No hyperbolic compact spaces Discussion with Jeff Weeks, in progress

Cosmology with CMB & LSS:

Cosmology with CMB & LSS: the Early universe VSP08 lecture 4 (May 12-16, 2008) Tarun Souradeep I.U.C.A.A, Pune, India Ω +Ω +Ω +Ω + Ω +... = 1 0 0 0 0... 1 m DE K r r The Cosmic Triangle (Ostriker & Steinhardt)