Dark Matter Properties and the CMB. Michael Kopp in collaboration with Dan Thomas and Costas Skordis

Transcription

1 Dark Matter Properties and the CMB Michael Kopp in collaboration with Dan Thomas and Costas Skordis

2 Outline Generalized dark matter, ΛGDM Connection to thermodynamics and fluids Initial conditions and CMB Fisher estimates including the 3 new parameters

3 Believing in dark matter High prior from particle physics axions wimps LSP sterile ν Low prior for modified gravity CDM gives consistent picture within General Relativity Gravitational force points to places where baryons cannot be but where CDM is expected Only ugly versions of relativistic MOND. Excellent agreement of GR with experiment. Internal galaxy and cluster dynamics Large scale structure Lensing CMB BBN Bullet cluster CMB peak structure

4 Generalised dark matter T µν = ρu µ u ν +(ρ + P )g µν + Σ µν Cold and Collisionless matter in the continuum limit is described before shell crossing as perfect fluid with P= A perfect fluid can have pressure P. Usually P=P( ). We allow for special intrinsic entropy perturbations or non-adiabatic pressure Choose uμ to be Landau-Lifshitz frame: u µ T µ ν = ρu ν Σμν is the transverse and traceless shear, no heat flux. T µ ν = T g µν + T Λ µ ν + T SM µ ν

5 Generalised dark matter Linear perturbation theory ds = a (1 + Ψ)dτ i ζdτdx i + ( h)γ ij + D ij ν dx i dx j ρ = ρ(1 + δ) P = ρ(w + Π) u = a(1 + Ψ) u i = a i θ D ij = i j 1 3 γ ij Σ i j = ρ(1 + w)d ij Σ GDM energy momentum conservation δ g =3H (wδ g Π g ) (1 + w) k (θ g ζ)+ 1 ḣ θ g = (1 3c a)hθ g w Π g k 3κ Σ g + Ψ 3 GDM closure relations W. Hu 1998 ApJ 56 continuity + Euler g for GDM made-up µ T g µν = Π g = c sδ g +(c s c a)3h(1 + w)θ g 4 Σ g = 3HΣ g + (1 + w) c vis(θ g ζ 1 ν) Blas et al 11 JCAP 7 c s = c s(k, τ) c vis = c vis(k, τ) w(τ) P g ρ g P c g a(τ) ρ g = w ẇ 3H(1 + w)

6 1 GDM connection to thermodynamics and coupled fluids

7 GDM from Thermo Review of LL Landau, Lifshitz Vol 6 P = p + P vis (Relation between pressure and thermodynamical pressure and bulk viscosity) ρ + p =st + µn (s: entropy density, μ: chemical potential, dρ =Tds+ µdn (Gibbs relation) n: particle density) dp =sdt + ndµ (Gibbs Duhem relation). T α ν =(µn + Ts)u α u ν + P vis u α u ν + pg α ν + Σ α ν Just the energy momentum tensor N ν = nu ν + j ν S ν su ν µ u ν α T α ν N ν = ν = T jν ν S ν = j ν µ ν T 1 T Σα ν α u ν P vis T νu ν Σ αν = η LL α α ν ν (α u ν ) TF P vis = ζ LL β u β j ν = κ LL α ν α µ T, ν S ν Required by common sense and H-theorem

8 GDM from Thermo Linear perturbation theory 4 Σ g = (1 + w) c vis(θ g ζ ν/) 3HΣ g Σ LL = aη LL (θ ζ ν/) ρ(1 + w) δα ᾱ = θ j κ LL ᾱ P vis + ρπ vis = ζ LL 1 a N ν = nu ν + j ν j i =: i j 3k g w, c s.1, k.1 Mpc 1 α µ T 3H(1 Ψ)+ḣ/ (θ ζ) c vis.1 c vis,alg Τ Mpc P = p + P vis c s = p,ρ α p = p(ρ, α) Π = c sδ + c s c δα a 3H(1 + w) ᾱ + Π vis c s c a = ᾱ ρ p,α ρ Exactly GDM if δα ᾱ = θ κ LL j Π vis = ζ LL =

9 GDM from two fluids T µ ν = T g µν + T Λ µ ν + T SM µ ν T g µν = T 1 µ ν + T µ ν T 1 µ ν = ρ 1 (1 + w 1 )u 1 µ u 1 ν + w 1 ρ 1 δ µ ν 1,: tightly coupled perfect fluids µ T µ ν = J ν = µ T 1 µ ν Q J S 1 = q δj S,i = δj i Π g = c a Q= δ g + w 1Q ρ g θ g + w 1R(1 + w) 1 δ 1 1 δ Q 1+w 1 1+w components Example: baryon-photon fluid, Q= :Photon, :Baryon, k.1 Mpc 1 (1 + R) S 1 w1 = w 1 w 1 ρ 1 (1 + w 1 ) + 1 θ g ρ (1 + w ) c a g nad Ε s x R = (1 + w ) ρ (1 + w 1 ) ρ 1 q Hτ c S 1 τ c H 1 c s = c a Q= c s c a = w 1 Q 3 ρ g H(1 + w) GDM

10 GDM from... Particles (Boltzmann equation) Freely streaming warm dark matter Specific models, like self interacting massive neutrinos and dark atoms + dark photons Fields (effective or fundamental) Axion condensates. Armendariz-Picon, Neelakanta, JCAP 14 Oldengott et al JCAP 15 Cyr-Racine, Sigurdson, PRD 13 Sikivie, Yang, PRL 9 Effective theory of CDM on large scales (larger than the non-linear scale): Leads to Landau-Lifshitz type energy momentum tensor, including bulk viscosity Baumann et al, JCAP 1 Mimetic dark matter and more general constrainednorm scalar field theories. Mirzagholi, Vikman, arxiv 15 Ballesteros, JCAP 15

11 GDM: initial conditions and CMB

12 Initial conditions Bucher et al PRD 6 Ansatz for x = kτ 1 w,c η = η + η 1 x + ε(η (ε) s = O() 1 1 x + η(ln,ε) 1 x ln x)+η x + ε(η (ε) x + η (ln,ε) x ln x)... δ g = δ g, + εδ (ln,ε) g, ln x + δ g,1 x + ε(δ (ε) c,1 x + δ(ln,ε) g,1 x ln x)+... I = {η, δ b,, δ c,, δ γ,,v γ,, δ ν,,v ν,, σ ν,, δ g,,v g,, σ g, } Task 1: find the maximal subset Imodes of I that can be chosen independently C l bi Cl gi Brute force method: simply considered all possible subsets of I found: 1.5 I modes = {η, δ g,, δ b,, δ c,, δ ν,,v ν, } w, c vis, baryon vs GDM isocurvature c s. c s.1 Baryon and GDM isocurvature modes are no longer identical l 11 1st order ODEs Task : find all coefficients as function of Imodes Test 1: Taking the ansatz up to x n, the two unused trace and traceless Einstein equations are solved up to x n-1. Test : Exact numerical solution tracks analytical solution

13 Effects on CMB.8 k.65 Mpc 1, c s, c vis based on a modified code Lesgourgues c s, c vis ll 1C l Π T ll 1C l Π T w w. w. Planck Τ Mpc k.65 Mpc 1, c s, c vis l.7 w means GDM density during decoupling Τ Mpc k.65 Mpc 1, c s, c vis w is anticorrelated with ωg Late ISW effect is negligible Calabrese et al, PRD Τ Mpc

14 Effects on CMB.8 based on a modified code Lesgourgues 11.6 k.65 Mpc 1, w w c s, c s.1, c s, c vis c vis c vis Τ Mpc ll 1C l Π T ll 1C l Π T Planck.5. k.65 Mpc 1, w k.65 MpcΤ 1 Mpc, w.1 1 c means Φ decays cs is anticorrelated with cvis Late ISW effect is strong l Τ Mpc

15 w k ns ln1 1 As Τ Ω Ωg Ωb Fisher Matrix TT Planck 15 fiducial ln1 1 As ns ln1 1 A s ns ln1 1 A s k w F ij = n s n s w k l= k 1 δc l w C l i δw = C l j c s c vis n s k w δc s = Preliminary n s k w c s Ω b Ω g Ω Τ c s c vis ln1 1 A s n s c s c vis k c s c vis w c s c vis c s c vis δc vis = c vis Xu, Chang, PRD 88, 13 w =(.7 ±.8) 1 3

16 Summary Generalized dark matter with 3 new parameters offers the possibility to test dark matter properties in the CMB: warm + free streaming, interacting, condensate, mimetic dark matter... GDM connection to thermodynamics and fluids Worked out initial conditions CMB with modified Fisher estimates including the 3 new parameters ongoing: Use MCMC with Planck likelihood and lensing for GDM parameter estimation. ongoing: Map specific models to GDM parameters