The Cosmic Microwave Background and Dark Matter Constantinos Skordis (Nottingham) Itzykson meeting, Saclay, 19 June 2012
(Cold) Dark Matter as a model Dark Matter: Particle (microphysics) Dust fluid (macrophysics) Particle (PDM) Nongravitational detection (perhaps, perhaps, perhaps) DAMA, CoGeNt, Crest? Extremely successful for LSS, CMB, clusters Dust fluid ( CDM) Λ Potential problems for galaxies (cuspy halos..., satellites...,) Need Dark Energy Λ
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 Does a dust fluid imply particle dark matter? Can a modification of gravity produce similar effects
Why CMB indicates CDM WMAP satellite 7year data (2009) third peak
CMB angular power spectrum ˆn ˆn θ Θ(ˆn)Θ(ˆn ) = l (2l + 1)C l P l (cosθ) P l (µ) : Legendre polynomials C l : Angular power spectrum angular eigenfunctions µ =[ 1, 1] Functions defined in [ 1, 1] can be expanded in terms of P l (µ)
Fluctuations in the Universe Metric fluctuations ds 2 = a 2 [ (1 + 2Ψ)dτ 2 + (1 2Φ)d x d x ] Two Newtonian potentials: Φ(τ,k) Ψ(τ,k) (in Fourier space) Fluids: Density contrast: δ δρ ρ Velocity u i = a i θ δ(τ,k) θ(τ,k) (adiabatic) Pressure fluctuation: δp = c 2 aδρ Shear σ Adiabatic speed of sound Baryons and Cold Dark Matter Photons and massless neutrinos Massive neutrinos 0 c 2 a 1 3 c 2 a =0 c 2 a = 1 3
CMB description (ignoring polarization effects) CMB Temperature contrast: Θ(τ, k, ˆp) Boltzmann equation Θ + ikµθ Φ + ikµψ = an e σ T [Θ 0 Θ + ikµθ b ] Fourier mode ˆk ˆp photon propagation µ = ˆk ˆp Compton scattering Θ(τ, k, ˆp) =Θ(τ, k, µ) Expand in multipole moments: Θ(τ, k, µ) = l (2l + 1)Θ l (τ,k)p l (µ) Angular Power Spectrum C l = 2 π dkk 2 P 0 (k) Θ l (τ 0,k) 2
Tightcoupling and Freestreaming Tightcoupling: Compton scattering + ++ + + + ++ + + τ Recombination + + + ++ + ++ + + Freestreaming
Solving the Boltzmann equation τ < τ Tightcoupling: Θ 0 + R 1+R } Damped harmonic oscillator ȧ a Θ 0 + k 2 c 2 sθ 0 = k2 3 Ψ + Φ + R 1+R } Φ forced by gravity, ȧ a Φ (Hu & Sugiyama 1996) Ψ Θ 0 (τ,k) R = 3ρ b 4ρ γ : Baryonphoton ratio c 2 s = 1 3(1+R) : Baryonphoton fluid sound speed τ > τ Freestreaming: Θ(τ 0, k, µ) =e ikµ(τ τ 0 ) [Θ 0 + Ψ ikµθ b ]+ Effective temperature Θ 0 + Ψ Doppler Primary anisotropies ikµθ b } Θ + ikµθ Φ + ikµψ =0 (ignore from now on) τ0 τ dτe ikµ(τ τ 0) } ( Φ + Ψ) Integrated SachsWolfe effect (ISW)
Goodness of the approximation No source term no CDM Exact result (no approximation) Source = k2 3 Ψ Full source term with CDM (same colours as above)
Silk damping Breakdown of tightcoupling Random walk: λ D λ MF P N 1 ne σ T H Θ 0 + Ψ e k/k D (Θ 0 + Ψ) Typical values: for Ω b h 2 =0.02 k D 0.12Mpc 1 k D 0.45Mpc 1 for Ω b h 2 =0.22 exact k D Θ 0 + Ψ 2 tightcoupling not very relevant for first 3 peaks k
Acoustic peaks Assume constant potentials, WKB solution: (Hu & Sugiyama 1996) Θ 0 + Ψ = RΨ + A cos(kr s ) effective temperature = baryon drag + adiabatic mode oscillation at LSS Oscillation frequency given by sound horizon r s = c s dτ Oscillation zeropoint displaced by gravity RΨ
The baryon drag (Hu & Sugiyama 1996) Θ 0 + Ψ = RΨ + A cos(kr s ) C Θ 0+Ψ l increasing baryon density R = 3ρ b 4ρ γ
CMB for Baryononly Universe Ω b =1 h =0.7 Ω b 0.04 Ω Λ 0.96 Why aren t peak heights alternating?
Potential evolution Radiation era Φ +4ȧ a Φ + k2 3 Φ =0 Φ = sin(kτ/ 3) kτ cos(kτ/ 3) k 2 τ 2 oscillatory decay Matter era Φ +3 ȧ a Φ =0 Φ = const no CDM with CDM at LSS total Φ photon contr. CDM contr. with CDM baryon contr. τ/τ τ/τ Ω b h 2 =0.22 Ω b h 2 =0.02 Ω c h 2 =0.2 no CDM k
Potential decay no CDM with CDM Φ 2nd Φ 2nd Θ +Ψ Θ +Ψ 1st 1st τ τ Ω b h 2 =0.02 Ω c h 2 =0 Ω b h 2 =0.02 Ω c h 2 =0.2
Acoustic driving (Hu & Sugiyama 1996) Ω b h 2 =0.02 Ω c h 2 =0 Φ 2nd Φ 2nd Ω b h 2 =0.02 Ω c h 2 =0.2 Θ +Ψ 1st Θ +Ψ 1st C Θ+Ψ l reducing matter density driving due to potential evolution during tightcoupling 2nd Θ 0 + R 1+R ȧ a Θ 0 + k 2 c 2 sθ 0 = k2 3 Ψ + Φ + R 1+R ȧ a Φ 3rd
ISW effect Ω b h 2 =0.02 Ω c h 2 =0 Φ 2nd Φ 2nd Ω b h 2 =0.02 Ω c h 2 =0.2 Θ +Ψ 1st Θ +Ψ 1st C ISW l reducing matter density ISW Due to potential evolution during freestreaming Θ ISW l (τ 0,k)= τ0 ( dτj l [k(τ 0 τ)] Φ + Ψ) τ this is early ISW occurs just after recombination nothing to do with dark energy
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 effect of CDM
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
Generalized Dark Matter (Hu 1998) Background equation of state w 0, may also be timevarying Nonadiabatic speed of sound: Shear viscosity Hu et al. 1998 c vis c s c a obtained from effective shear δp = c 2 sδρ +3ȧ a (c2 s c 2 a)(ρ + P )θ σ (modelled after neutrinos) Li et al. 2008: assume background CDM, but general pressure perturbation and shear. parameterize growing mode of CDM certain engineered δp and σ after LSS give identical spectra to standard CDM Calabrese et al. 2009 Λ
Alternative to ΛCDM? Phys. Rep. 513, 1 (2012)
Modified gravity and the CMB Equality: New dof may change the background Potential evolution depends on Modified Einstein equations. Any potential decay during tightcoupling (before recombination) drives the anisotropies Any potential decay after recombination boosts anisotropies due to the Integrated SachsWolfe effect
EddingtonBornInfeld theory (Banados 2009) GR g tr[q 1 g] GR q two metrics two sectors of GR matter Describes a massless and a massive graviton m H 0 10 33 ev ρ q ρ 0 a 3 ρ q const
Perturbations: DM with stress (Bañados, Ferreira, C.S. 2009) 2nd metric has 4 new dof map them into δ, θ, δp, σ Perturbations behave like CDM on small scales pressure perturbation shear δp 0 σ 0 Instability ISW
Posing as ΛCDM Instability due to BoulwareDeser ghost Can be curbed by reintroducing bare Λ (Bañados, Ferreira, C.S. 2009) but ghost remains theory is not good
Parameterizing deviations from GR Inspired by PPN Add terms to Einstein equations involving new dof and potentials C.S. (2009) T. Baker, P. Ferreira, C.S., J. Zuntz(2011) (similar to Batteye & Pearson 2012) we can always reshufle any set of field equations to look like : δg µν =8πGδT (known) µν + δu µν Parameterize δu µν by requiring diffeo inv. and upto two time derivatives 1 Metric GI variables: ˆΦ and ˆΓ = k New dof: ˆχ and ˆ χ ( ˆΦ + ȧ ) a ˆΨ contain only 1 time derivative Bianchi identity determines field equations for new dof Solve to get CMB spectrum + P(k)
Parameterization (0,0) Required by diff. inv. (no freedom) (0,i) traced (i,i) traceless (i,j)
Toy case: no extra fields Assume background unchanged (0,0) (0,i) traced (i,i) traceless (i,j) Further condition to avoid instability: One function of time remains
Potential engineering Potentials constant during matter era: Two parameters: departures from constancy during matter era radiation era modification Initial conditions different from LCDM Work in progress...
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 Linear Effective CDM equations do not imply particle DM. Difficult to have radical departures from CDM (anything non CDM leads to potential evolution), but need to be quantified.