The Cosmic Microwave Background and Dark Matter

Transcription

1 The Cosmic Microwave Background and Dark Matter (FP7/ ) / ERC Consolidator Grant Agreement n Constantinos Skordis (Institute of Physics, Prague & University of Cyprus) Paris, 30 May 2017

2 Motivation Best evidence for CDM comes from CMB CMB described by linear theory No messy astrophysics Very accurate observations Effects of CDM on CMB Pedagogical Can help to test properties of dark matter Can help to test GR A dust fluid does NOT imply particle dark matter. (EddingtonBornInfeld in yesterday s talk)

3 Why CMB indicates CDM third peak Planck Collaboration, 2015

4 CMB description CMB Temperature contrast: Boltzmann equation (, k, ˆp) = T/ T (ignoring polarization effects) + ikµ + ikµ = ane T [ 0 + ikµ b ] Fourier mode ˆk µ = ˆk ˆp ˆp photon propagation Compton scattering ) (, k, ˆp) = (,k,µ) Expand in multipole moments: (,k,µ)= X` (2 + 1) `(,k)p`(µ) Angular Power Spectrum C` = 2 Z dkk 2 P 0 (k) `( 0,k) 2

5 Tightcoupling and Freestreaming Tightcoupling: + Compton scattering Recombination Freestreaming

6 Freestreaming > Boltzmann: + ikµ + ikµ =0 ) ( 0,k,µ)=e ikµ( 0) [ 0 + ikµ b ]+ Primary anisotropies Z 0 d e ikµ( 0) + Integrated SachsWolfe effect (ISW) Effective temperature 0 + Doppler ikµ b ignore lspace: ( 0,k,µ)! `( 0,k) ) ( 0,k)=j [k( 0 )] [ 0 + ikµ b ]+ Z 0 d j [k( 0 )] +

7 Tightcoupling < Expand in powers of (an e T ) 1 Only 0 1 relevant. (Hu & Sugiyama 1996) ) 0 + R 1+R } Damped harmonic oscillator ȧ a 0 + k 2 c 2 s 0 = k R 1+R R = 3 b 4 : Baryonphoton ratio c 2 s = 1 3(1+R) } ȧ a forced by gravity, : Baryonphoton fluid sound speed no CDM with CDM No source term Source = k2 3 Full source term Exact result (no approximation)

8 Acoustic peaks Constant potentials, WKB solution: 0 + = R + A cos(kr s ) at LSS Zeropoint displaced by gravity Frequency: sound horizon r s = c s d Increasing baryon density C 0 + `

9 Silk damping Breakdown of tightcoupling Random walk: D MFP p N 1 p ne T H 0 + e k/k D ( 0 + ) Damping coefficient k D 0.12Mpc 1 k D 0.45Mpc 1 for for bh 2 =0.02 bh 2 =0.22 exact k D tightcoupling not very relevant for first 3 peaks

10 CMB for Baryononly Universe b =1 h =0.7 b Why aren t peak heights alternating?

11 Potential evolution Radiation era ȧ +4 a + k2 3 =0 ) = sin(k / p 3) k cos(k / p 3) k 2 2 oscillatory decay Matter era +3 ȧ a =0 ) = const no CDM with CDM at LSS total photon contr. CDM contr. with CDM baryon contr. / / k bh 2 =0.22 bh 2 =0.02 ch 2 =0.2 no CDM

12 Potential decay no CDM with CDM 2nd 2nd + 1st 1st + bh 2 =0.02 ch 2 =0 bh 2 =0.02 ch 2 =0.2

13 Acoustic driving (Hu & Sugiyama 1996) bh 2 =0.02 ch 2 =0 2nd 2nd bh 2 =0.02 ch 2 = st 1st + C + reducing matter density driving due to potential evolution during tightcoupling 2nd 0 + R 1+R ȧ a 0 + k 2 c 2 s 0 = k R 1+R ȧ a 3rd

14 ISW effect bh 2 =0.02 ch 2 =0 2nd 2nd bh 2 =0.02 ch 2 = st 1st + C ISW reducing matter density ISW Due to potential evolution during freestreaming ISW ( 0,k)= Z 0 d j [k( 0 )] + this is early ISW occurs just after recombination nothing to do with dark energy

15 CDM effect on CMB Baryons raise odd peaks relative to even peaks Increasing CDM density, moves equality forward in time Potentials decay during radiation era, constant in matter era Potential decay during tightcoupling (before recombination) drives the anisotropies Potential decay after recombination boosts anisotropies due to the Integrated SachsWolfe effect GR+baryons CDM TeVeS effect of CDM

16 Beyond CDM Properties of dark matter: Generalized Dark Matter (W. Hu 1998)! Assume CDM but test GR! Try to replace CDM with a modification of GR

17 Generalised Dark Matter model W. Hu (1998) Defined for FRW + linear perturbations general background eq. of state w(a) two perturbative functions: sound speed c 2 s(a, k) and (shear) viscosity c 2 vis(a, k) Standard equations for density contrast and velocity divergence Closure equations for: Pressure perturbation P = c2 s + 3(1 + w)(c 2 s c 2 a)ȧ a Shear = 3 ȧ a w c2 vis (CN) Phenomenological: to close the Boltzmann hierarchy

18 Relating GDM to realistic theories M. Kopp, D. Thomas, CS, PRD 94, (2016) GDM realised in: Scalar fields Nonequilibrium thermodynamics Tightlycoupled fluids Effective field theory of fluids Effective field theory of Large Scale Structures

19 Brief GDM phenomenology M. Kopp, D. Thomas, CS, PRD 94, (2016) q Decay scale k 1 d ( ) c 2 s c2 vis Expect degeneracy for c 2 s c2 vis = const Jeans scale: k 1 J 0.2c e Case c vis c s and c vis k 1 ' A c 2 e 2 vis k2 2 /2 (c e k ) 1 J 1(c e k ), ) c 2 e 0 Effective speed of sound c 2 e c 2 2 s ) c 2 s 0 5 c2 vis Overdamping scale k 1 damp 0.18c vis q 1+ 15c2 s 8c 2 vis no oscillations for: c 2 vis & 0.57c 2 s

20 Potential decay M. Kopp, D. Thomas, CS, PRD 94, (2016) c 2 s c2 vis = k = k d k = k J 0.6 k = k damp F` c s 2 =0.0065, c s 2 =0.0084, c s 2 =0.01, 1 (k c vis ) 2 / c 2 vis = c 2 vis =0.003 c 2 vis = k t 3 D k = k d k = k J k = k damp z = 0, t > Mpc»F`» (k ) 2 e (k c vis ) 2 /2 (k ) +1/ k t

21 CMB Power spectra DTT T0 L D 5 2 DTT T0 L D Ratio1 c2vis no lensing Ratio1 0.2 tio1 c2s Ratio l l tio w Ratio M. Kopp, D. Thomas, CS, PRD 94, (2016) l

22 CMB Lensing M. Kopp, D. Thomas, CS, PRD 94, (2016) c 2 s,c 2 vis lhl+1l D l ff â w =0.01 fiducial CDM w = 7 T0D lhl+1l D l Tf D l 7 T 0L 2 D l

23 Constrains from cosmology: Datasets used D. Thomas, M. Kopp & CS, ApJ 830, 155 (2016) Planck 2015: TT + TE + EE + LowP : PPS + Planck 2015: Lensing + BAO + Riess et al. H 0

24 Results D. Thomas, M. Kopp & CS, ApJ 830, 155 (2016) PPS+Lens w BAO w g H 0 75 H CDM w g

25 Results D. Thomas, M. Kopp & CS, ApJ 830, 155 (2016)

26 Results D. Thomas, M. Kopp & CS, ApJ 830, 155 (2016) 0.8 GDM likes low 8 s c s 2

27 Results PPS: Planck TTTEEELowP D. Thomas, M. Kopp & CS, ApJ 830, 155 (2016) PPS + Lens % c vis c 2 s c2 vis = const c s % 99.7% 95.5% 99.7% 95.5% 99.7% 95.5% 99.7%

28 Timevarying equation of state 8 pixels in loga D. Thomas, M. Kopp, CS (arxiv:1707.xxxx) PPS + BAO 0.1 w % % 99% 99% constant w a

29 Conclusion 3rd peak in CMB spectrum appears raised: indication for CDM Why? Potentials decay during radiation domination Potentials stay constant during matter domination Potential decay enhances anisotropies through acoustic driving (tightcoupling) and ISW effect (freestreaming) CDM puts CMB into matter era least potential decay suppresses 1st and 2nd peak so that 3rd peak appears raised. Can be used to test nonstandard properties of CDM and test GR Very difficult (if not impossible) to have radical departures from CDM (anything non CDM leads to potential evolution)

30 Conclusion Natural to consider extensions of CDM, with nonzero equation of state, speed of sound and viscosity. Generalised Dark Matter (GDM) model (W. Hu) is a phenomenological model providing this. Realistic theories may be approximated by GDM under certain conditions. of which we highlight the effective appearance of GDM parameters from pure CDM through integrating out small wavelengths (EFT of LSS) Planck 2015 constrains constant GDM parameters: <w< c 2 s < at 99.7% CL c 2 vis <