A theorist s take-home message from CMB Supratik Pal

A theorist s take-home message from CMB Supratik Pal Indian Statistical Institute Kolkata

Outline CMB à la WMAP and Planck Inflation Dark energy New horizons 1

A cosmologist s wishlist To explain... 2

A cosmologist s wishlist To explain......uniquely! 2-a

The CMB sky CMB temperature T 0 = 2.725K at all directions The Universe is homogeneous and isotropic at largest scale How many parameters to describe the Universe? 6 (or 7?) J von Neumann: With four parameters I can fit an elephant and with five I can make him wiggle his trunk :) Are these 6 (or 7) parameters a bit too many? 3

All about CMB temperature Happenings at CMB: Anisotropy, Polarization, Distortion Background : T 0 = 2.725K Blackbody spectrum Fluctuations : 200µK < T < 200µK T rms 70µK T pe 5µK T pb 10 100nK 4

All about CMB temperature Happenings at CMB: Anisotropy, Polarization, Distortion Background : T 0 = 2.725K Blackbody spectrum Fluctuations : 200µK < T < 200µK T rms 70µK T pe 5µK T pb 10 100nK Temperature anisotropy T + two polarization modes E & B Four CMB spectra: C TT,Cl BB,Cl TE l,cl EE Parity violation/systematics Two more spectra: Cl TB,Cl EB 4-a

How to decode information? T(n) = a lm Y lm (n) 2-point correlation fn. C l = 1 2l+1 C l = dk k P R(k)T 2 l (k) alm 2 Peak positions, heights and ratios give cosmological parameters imprints of both early universe and late universe 5

Cosmological parameters from C l Fundamental/ fit parameters Ω b h 2 = baryonic matter density Ω c h 2 = dark matter density Ω X = dark energy density P R = primordial scalar power spectrum n s τ = scalar spectral index = optical depth r = tensor-to-scalar ratio Altogether 6 (or 7 if r 0) 6

Cosmological parameters from C l Fundamental/ fit parameters Ω b h 2 = baryonic matter density Ω c h 2 = dark matter density Ω X = dark energy density P R = primordial scalar power spectrum n s τ = scalar spectral index = optical depth r = tensor-to-scalar ratio Altogether 6 (or 7 if r 0) Derived parameters t 0, H 0, Ω b, Ω c, Ω m, Ω k, Ω tot, σ 8, z eq, z reion, A SZ,... 6-a

Best fit parameters WMAP 9 Planck P R (2.464±0.072) 10 9 (2.196 +0.051 0.060 ) 10 9 n s 0.9606±0.008 0.9603±0.0073 n s 0.023±0.001 0.013±0.009 r < 0.13 < 0.11 Ω b 0.04628±0.00093 Ω c 0.2402 +0.0088 0.0087 Ω b +Ω c = 0.315±0.017 Ω X 0.7135 +0.0095 0.0096 0.685 +0.018 0.016 τ 0.088±0.015 0.089 +0.012 0.014 H 0 69.32±0.80 km/s/mpc 67.3±1.2 km/s/mpc t 0 13.772±0.059 Gyr 13.817±0.048 Gyr WMAP9 and Planck give consistent results 7

How sensitive to parameters the CMB TT plot is? 8

Inflation from CMB Lagrangian density L φ = 1 2 φ 2 V(φ) EM tensor components ρ φ = 1 2 φ 2 +V(φ) ; p φ = 1 2 φ 2 V(φ) Choose the potential to be sufficiently steep so that V V/V 2 1 Scalar field rolls down the potential : Tracker potential Governing equations H 2 8π 3M 2 P V(φ) 3H φ+v (φ) 0 Guth; Linde; Starobinsky; Liddle; Lyth; Sahni... 9

Adiabatic, Gaussian initial perturbations Adiabatic all species share a common perturbation Gaussian Gaussian random distribution, stochastic properties completely determined by spectrum 10

Adiabatic, Gaussian initial perturbations Adiabatic all species share a common perturbation Gaussian Gaussian random distribution, stochastic properties completely determined by spectrum Harrison-Zeldovich spectrum P R (k) P R (k 0 )( k k 0 ) n s 1 P R (k 0 ) V(φ) φ direct reflection on inflationary models P R 10 9 small initial fluctuations 10-a

Adiabatic, Gaussian initial perturbations Adiabatic all species share a common perturbation Gaussian Gaussian random distribution, stochastic properties completely determined by spectrum Harrison-Zeldovich spectrum P R (k) P R (k 0 )( k k 0 ) n s 1 P R (k 0 ) V(φ) φ direct reflection on inflationary models P R 10 9 small initial fluctuations (n s 1) = small nearly scale invariant power spectrum (n s 1) dv dφ, d2 V dφ 2 0 V(φ) slowly varying (quasi-ds) confirms perturbations originated from dynamics of scalar field: proof of inflationary paradigm 10-b

Adiabatic, Gaussian initial perturbations Adiabatic all species share a common perturbation Gaussian Gaussian random distribution, stochastic properties completely determined by spectrum Harrison-Zeldovich spectrum P R (k) P R (k 0 )( k k 0 ) n s 1 P R (k 0 ) V(φ) φ direct reflection on inflationary models P R 10 9 small initial fluctuations (n s 1) = small nearly scale invariant power spectrum (n s 1) dv dφ, d2 V dφ 2 0 V(φ) slowly varying (quasi-ds) confirms perturbations originated from dynamics of scalar field: proof of inflationary paradigm Modified spectrum P R (k) P R (k 0 )( k k 0 ) n s 1+n s ln(k/k s) n s 0 deviation from power law / scale invariance 10-c

Matches almost all the points for different l But outliners at l = 22,40 step function? lensing? new physics?? [ ] e.g.: Step function V(φ) V(φ) 1+αtanh φ φ 0 φ Souradeep, JCAP:2010 11

Gravitational waves A small fraction of the CMB photons get polarized due to quadrupole anisotropies. Generates 2 polarization modes (E & B) B modes Gravitational waves + NG + Lensing... Detection of gravitational waves have direct reflection on energy scale of inflation (hence on fundamental physics) 12

Gravitational waves A small fraction of the CMB photons get polarized due to quadrupole anisotropies. Generates 2 polarization modes (E & B) B modes Gravitational waves + NG + Lensing... Detection of gravitational waves have direct reflection on energy scale of inflation (hence on fundamental physics) Feb 2014: r < 0.13 energy scale of inflation < 2 10 16 GeV Can at best rule out a class of models (e.g. V = λφ 4 ) which predict large r 12-a

Gravitational waves A small fraction of the CMB photons get polarized due to quadrupole anisotropies. Generates 2 polarization modes (E & B) B modes Gravitational waves + NG + Lensing... Detection of gravitational waves have direct reflection on energy scale of inflation (hence on fundamental physics) Feb 2014: r < 0.13 energy scale of inflation < 2 10 16 GeV Can at best rule out a class of models (e.g. V = λφ 4 ) which predict large r > Feb 2014: r 0.2 energy scale of inflation 10 16 GeV Controversy not yet settled. If confirmed, a direct proof of inflation. 12-b

Inflationary models (confronted with WMAP7) Choudhury, SP, PRD:2012, JCAP:2012, NPB:2013 Pal, SP, Basu, JCAP:2010, JCAP:2012 Field equations are different for different cases! Brane V(φ) = V 0 [1+ ( ( ))( ) ] 4 D 4 +K 4 ln φ φ M M 1.234 < 10 9 P S < 3.126 ; 0.936 < n S < 0.951 2.176 < 10 5 r < 4.723 ; 0.798 < 10 3 α S < 1.345 Galileon V(φ) = [ ( )] 2 m= 2( 1) C 2m 1+D 2m ln φ M φ 2m 2.401 < 10 9 P S < 2.601 ; 0.964 < n S < 0.966 0.215 < r < 0.242 ; 2.240 < 10 3 α S < 2.249 13

6000 CMB TT Angular Power Spectrum (For Scalar) WMAP7 D3 DBI Galileon ΛCDM+tens 150 CMB TE Angular Power Spectrum (For Scalar) WMAP7 D3 DBI Galileon ΛCDM+tens 5000 100 4000 50 l(l+1)c l /2π[µK 2 ] 3000 l(l+1)c l /2π[µK 2 ] 0 2000-50 1000-100 0 1 10 100 1000 l -150 0 200 400 600 800 1000 1200 l 60 50 CMB EE Angular Power Spectrum (For Scalar) WMAP7 D3 DBI Galileon ΛCDM+tens 100 CMB TT Angular Power Spectrum (For Tensor) D3 DBI Galileon(TT Mode) ΛCDM+tens(TT Mode) 40 l(l+1)c l /2π[µK 2 ] 30 20 l(l+1)c l /2π[µK 2 ] 10 10 0-10 0 200 400 600 800 1000 1200 l 1 10 100 l 14

Planck highlights Francis, 2013 15

Boring universe (6 parameters suffice) Little bit older universe (13.771 Gyr 13.817 Gyr) Confirms 3 neutrino species removes doubt from WMAP 16

Boring universe (6 parameters suffice) Little bit older universe (13.771 Gyr 13.817 Gyr) Confirms 3 neutrino species removes doubt from WMAP Higher resolution better estimate of n s 1 inflation More matter, less energy (higher 3rd peak) Peaks at high l direct evidence of BAO r < 0.11 GW yet undetected 16-a

Boring universe (6 parameters suffice) Little bit older universe (13.771 Gyr 13.817 Gyr) Confirms 3 neutrino species removes doubt from WMAP Higher resolution better estimate of n s 1 inflation More matter, less energy (higher 3rd peak) Peaks at high l direct evidence of BAO r < 0.11 GW yet undetected Outliners are still there physical origin, not from systematics Large scale anomalies : 10% deficit of signal, hemispherical asymmetry Big cold spot superstructure? 16-b

Modeling inflation in the light of Planck Choudhury, Majumdar, SP, JCAP(2013) Inflection point inflation from MSSM V(φ) = α+β(φ φ 0 )+γ(φ φ 0 ) 3 +κ(φ φ 0 ) 4 + 6.5 10 9 SHAPE OF THE POTENTIAL V Φ in M PL 4 6. 10 9 5.5 10 9 5. 10 9 4.5 10 9 0.0 0.2 0.4 0.6 0.8 1.0 Φ in M PL 2.092 < 10 9 P S < 2.297 ; 0.958 < n S < 0.963 r < 0.12 ; 0.0098 < α S < 0.0003 17

Planck+WMAP9+BAO: Blue: ΛCDM+r(α S ), Red: ΛCDM+r +α S 18

Planck+WMAP9+BAO: Blue: ΛCDM+r(α S ), Red: ΛCDM+r +α S 3000 CMB TT Angular Power Spectrum (for low l) PLANCK [With maximum errorbar] PLANCK [With minimum errorbar] INFLECTION POINT MODEL 6000 CMB TT Angular Power Spectrum (for high l) PLANCK INFLECTION POINT MODEL 2500 5000 2000 4000 l(l+1)c l TT /2π(in µk 2 ) 1500 1000 l(l+1)c l TT /2π(in µk 2 ) 3000 2000 500 1000 0 1 10 l 0 100 1000 l Good fit with Planck for both low and high l 18-a

Dark energy from CMB Cosmological constant ρ Λ = const. p Λ = ρ Λ Dark energy ( ρ X exp 3 ) z 1+ω(z) 0 1+z dz p X = ω(z)ρ X δρ Λ = 0 δρ X 0 19

Dark energy from CMB Cosmological constant ρ Λ = const. p Λ = ρ Λ Dark energy ( ρ X exp 3 ) z 1+ω(z) 0 1+z dz p X = ω(z)ρ X δρ Λ = 0 δρ X 0 Reflections in CMB CMB shift parameter (position of peaks) Integrated Sachs-Wolfe effect 19-a

Shift Parameter DE Shift in position of peaks by Ω m D D= Angular diameter distance (to LSS) Shift Parameter Ω R = m h 2 Ω k h χ(y) 2 χ(y) = siny(k < 0) ; = y(k = 0) ; = sinhy(k > 0) y = Ω k z dec o dz Ω m (1+z) 3 +Ω k (1+z) 2 +Ω X (1+z) 3(1+ω X ) 20

Shift Parameter DE Shift in position of peaks by Ω m D D= Angular diameter distance (to LSS) Shift Parameter Ω R = m h 2 Ω k h χ(y) 2 χ(y) = siny(k < 0) ; = y(k = 0) ; = sinhy(k > 0) y = Ω k z dec o dz Ω m (1+z) 3 +Ω k (1+z) 2 +Ω X (1+z) 3(1+ω X ) Hence, for k = 0 R = Ω m H 2 0 zdec o dz H(z) Hence calculate χ 2 CMB (ω X,Ω m,h 0 ) = [ ] 2 R(zdec,ω X,Ω m,h 0 ) R σ R + low z results (SNIa, BAO, OHD...) and find combined χ 2 = χ 2 i 20-a

DE change in angular diameter distance and shift parameter 21

Is CMB constraint on shift parameter model independent? Model R l a ΛCDM 1.707 ± 0.025 302.3 ± 1.1 wcdm (c 2 DE wcdm (c 2 DE = 1) 1.710±0.029 302.3±1.1 = 0) 1.711±0.025 302.4±1.1 ΛCDM m ν > 0 1.769±0.040 306.7±2.1 ΛCDM N eff 3 1.714±0.025 304.4±2.5 ΛCDM Ω k 0 1.714±0.024 302.5±1.1 w(z)cdm CPL (c 2 DE = 1) 1.710±0.026 302.5±1.1 ΛCDM + tensor 1.670 ± 0.036 302.0 ± 1.2 ΛCDM + running 1.742 ± 0.032 302.8 ± 1.1 ΛCDM + running + tensor 1.708±0.039 302.8±1.2 ΛCDM + features 1.708 ± 0.028 302.2 ± 1.1 Melchiorri, PRD:2008 22

Integrated Sachs-Wolfe Effect Some CMB anisotropies may be induced by passing through a time varying gravitational potential linear regime: integrated Sachs-Wolfe effect non-linear regime: Rees-Sciama effect 23

Integrated Sachs-Wolfe Effect Some CMB anisotropies may be induced by passing through a time varying gravitational potential linear regime: integrated Sachs-Wolfe effect non-linear regime: Rees-Sciama effect Poisson equation 2 Φ = 4πGa 2 ρδ Φ constant during matter domination time-varying when dark energy comes to dominate (at large scales l 20) C l = dk k P R(k)T 2 l (k) Tl ISW (k) = 2 τ dφ dηexp dη j l(k(η η 0 ) 23-a

But... Huge error bars! Perturbations in dark energy can remove degeneracy. 24

Dark energy in the light of Planck Hazra,... SP,..., 1310.6161 Used 3 different parametrizations: CPL, SS, GCG Analysis is robust CPL SS GCG w 0 /( A) 1.09 +0.168 0.206 1.14 +0.08 0.09 0.957 +0.007 0.043 w a /α 0.27 +0.86 0.56-2.0 +0.29 unbounded Ω m 0.284 +0.013 0.015 0.288 +0.012 0.013 0.304 +0.009 0.011 H 0 71.2 +1.6 1.7 70.3 +1.4 1.4 67.9 +0.9 0.7 25

1 CPL model Planck+WP non-cmb Planck+WP+non-CMB 1 CPL model Planck+WP non-cmb Planck+WP+non-CMB 1 SS model Planck+WP non-cmb Planck+WP+non-CMB Likelihood 0.5 Likelihood 0.5 Likelihood 0.5 0-2 -1.5-1 -0.5 0 0.5 1 w 0 0-3 -2-1 0 1 2 3 w a 0-2 -1.5-1 -0.5 0 w 0 1 GCG model Planck+WP non-cmb Planck+WP+non-CMB 1 GCG model Planck+WP non-cmb Planck+WP+non-CMB Likelihood 0.5 Likelihood 0.5 0-1 -0.9-0.8-0.7-0.6 -A 0-3 -2-1 0 1 2 3 α Likelihood functions for different parameters of EOS 26

76 CPL model 76 GCG model SS model 74 74 74 72 72 72 H 0 70 H 0 70 H 0 70 68 68 68 66 66 66-1.6-1.4-1.2-1 -0.8-0.6 w 0-1 -0.95-0.9-0.85-0.8-0.75-0.7 w 0-1.4-1.3-1.2-1.1-1 -0.9 w 0 0.8 0.90 0.8 1.0 0.92 1.0 0.94 w 1.2 w w 1.2 0.96 1.4 0.98 1.4 1.6 0.0 0.5 1.0 1.5 2.0 z 1.00 0.0 0.5 1.0 1.5 2.0 z 1.6 0.0 0.5 1.0 1.5 2.0 z Planck shows tension with Λ at 1-σ PanSTARRS rules out Λ at 2.4σ low z result (Rest, 1310.3828) 27

New horizons Large scale anomalies Lensing Non-Gaussianity Magnetic field 28

Large scale anomalies 29

Large scale anomalies Modifications to inflation? (Carroll, PRD:2008) Earlier universe preceding Big Bang? (Efstathiou, ) Undiscovered source in solar system? (Yoho, PRD:2011) A nice review by Huterer, 1004.5602 29-a

Lensing Effects of lensing Broadening of peaks Non-Gaussianity 30

Lensing Effects of lensing Broadening of peaks Non-Gaussianity Why delensing? Better estimate of parameters B-modes: removes degenarcy (vide SPT results) 30-a

Lensing Effects of lensing Broadening of peaks Non-Gaussianity Why delensing? Better estimate of parameters B-modes: removes degenarcy (vide SPT results) To do Propose delensing techniques Wait for Planck polorization & CMBPol data 30-b

Delensing using matrix inversion technique Pal, Padmanabhan, SP, MNRAS:2014 0.04 Full-sky: Lensing Contribution Flat-sky: Lensing Contribution 0.16 Full-sky: Lensing Contribution Flat-sky: Lensing Contribution 0.12 0.02 0.08 C l TT /Cl TT 0 C l EE /Cl EE 0.04 0-0.02-0.04-0.04 0 400 800 1200 1600 l -0.08 0 400 800 1200 1600 l 0.1 Lensed BB Full-sky: Unlensed BB Flat-sky: Unlensed BB 0.06 Full-sky: Lensing Contribution Flat-sky: Lensing Contribution 0.08 0.04 l(l+1)c l BB /2π in µk 2 0.06 0.04 C l TE /(Cl TT Cl EE ) 1/2 0.02 0-0.02 0.02-0.04 0-0.06 0 400 800 1200 1600 l 0 400 800 1200 1600 l Fractional difference between lensed and unlensed power spectra 31

Non-Gaussianity Perturbations mostly Gaussian, described by 2-point correlation fn. If (small) non-gaussianities are present reflected via B modes 3- and 4-point correlation fn. bispectrum f NL & trispectrum g NL,τ NL WMAP7 10 < f NL < 74 ; 7.4 10 5 < g NL < 8.2 10 5 32

Non-Gaussianity Perturbations mostly Gaussian, described by 2-point correlation fn. If (small) non-gaussianities are present reflected via B modes 3- and 4-point correlation fn. bispectrum f NL & trispectrum g NL,τ NL WMAP7 10 < f NL < 74 ; 7.4 10 5 < g NL < 8.2 10 5 Why important? Maldacena limit single field ( f NL < 1) vs multifield ( f NL > 5) B modes = GW + NG + lensing Need to separate out NG for correct estimate of GW Suyama-Yamaguchi consistency relation between f NL & τ NL 32-a

Take-home message 6 parameter description of the universe Adiabatic, Gaussian initial perturbations Inflation confirmed, with a pinch of salt (anomalies!) Gravitational waves detected? Outliners yet unexplained Dynamical DE? Probe ISW Large scale anomalies need to be explained Need delensing for B modes Non-Gaussian features to be explored 33