The Dark Sector ALAN HEAVENS INSTITUTE FOR ASTRONOMY UNIVERSITY OF EDINBURGH AFH@ROE.AC.UK THIRD TRR33 WINTER SCHOOL PASSO DEL TONALE (ITALY) 6-11 DECEMBER 2009
Outline Dark Matter Dark Energy Dark Gravity
Dark Matter Numerical simulations of ΛCDM predict a universal NFW profile: ρ s ρ(r) = 2 r r s 1+ r r s Concentration index, c=r v /r s, should scale like M -0.1 Mandelbaum et al 2008 Neutrinos we did
Bullet cluster Challenges MOND, TeVeS Dark Matter Galaxies (Lensing) Markevitch et al 2002 Clowe et al 2004 Hot Gas (X-ray)
Self-interacting Dark Matter? Spergel and Steinhardt (2000): Self-interacting Dark Matter could remove cusps if σ/m ~ 0.05-0.5 m 2 /kg Bullet cluster σ/m < 0.12 m 2 /kg (Randall et al 2007) Caveat on Dark Matter conclusion: κ is proportional to surface density in GR, but not in general modified gravity models. Nevertheless, it is still a challenge to account for this map.
Dark Energy Measurable Effects of Dark Energy: Distance-redshift relation Growth rate of perturbations (via H(a)) Assumes GR
Direct probes of geometry: Supernovae Standard(isable) candles Brightness Time From Garcia- Bellido 2004 Apparent brightness luminosity distance
Supernova Hubble diagram Evidence for acceleration/cosmological constant Redshift
Conclusions from Supernovae Λ is non-zero Riess et al 2004
Shear Ratio Test γ 1 γ 2 Depends only on global geometry: Ω DE, Ω m and w. Observer Galaxy cluster/lens Apply to large signal from galaxy clusters (Jain & Taylor, 2003, Taylor et al 2007) z L z 1 z 2 Fig: A. Taylor
Lensing probes both growth and geometry CFHTLS: -1.18 < w < -0.88 (95%) Kilbinger et al (2009) NB Flat universe assumed
Pan-STARRS 1 plus Planck Parametrisation in terms of scale factor a: w(a) = w 0 + (1-a) w a Note: this may not be a good parametrisation for DE models. Studies show only a few components of w(a) can be measured. (Heavens et al MNRAS 2007)
Combining 3D lensing, CMB, BAO, SNe (10000 sq deg lensing survey: one third of PS1) Flat 3.5% accuracy on w at z=0 1% on w(z) at z~0.4 Caveats: nonlinear clustering; DE clustering
Dark Gravity Necessary to modify Einstein s original equations: G µν = 8πG c 4 T µν E.g. by including Dark Energy on right hand side, or including Λ on l.h.s. G µν Λg µν = 8πG c Dark Gravity means more 4 T µν general modifications to the l.h.s.
Actions Einstein s original field equations are equivalent to an action (ignoring some factors of G, π) S = d 4 x µ gr+ S source And with Λ: S = d 4 x µ g (R + Λ)+S source Generalisations [ f(r) models ]: S = d 4 x µ g [R + f(r)] + S source Can also add terms like or even R µν R µν R µναβ R µναβ
Modified G/Poisson equations Generically Φ and Ψ are different. Formally we can define the gravitational slip, by and the change to the effective G by The sum Ψ+Φ obeys where Ψ(k, a) =[1+(k, a)] Φ(k, a) k 2 Φ k =4πGQ(k, a) a 2 ρ m δ k k 2 (Ψ + Φ) k =2Σ 3H2 0 Ω m 2a Σ Q(1 + /2) δ k Daniel et al 2009 GR: Q=1; Σ=1; =0
Braneworld models Extra dimensions broadly inspired by string theory E.g. DGP (Dvali, Gabadadze, Porrati 2000) model S = 1 r c bulk Leads to a modified Friedmann equation H 2 H r c = 8πGρ 3 d 5 x µ R (5) + And modified Poisson equations: k 2 Φ k = 4πGa 2 1+ 1 ρ m δ k 3β k 2 Ψ k = 4πGa 2 1 1 ρ m δ k 3β brane d 4 x µ R (4) r 1 c = H 0 (1 Ω m ) β =1 2r c H 1+ Ḣ 3H 2 Growth rate of Newtonian potential is altered In this case, Φ+Ψ obeys the normal Poisson equation (Σ=1)
Summary of modified gravity effects Friedmann equation is altered, so Expansion history a(t), [or H(a)] is changed Geometry r(z) is changed Growth rate of matter fluctuations is altered Curvature and potential perturbations may behave differently Response of photons to density perturbations may change Are these measurable?
Modified Gravity or Dark Energy? Modified Gravity theory will give a certain H(a). We can always find an equation of state (strictly just p/ρ) to mimic this in GR: Solve for any given H(a). Exercise: which depends on H(a) via the critical density Supernovae cannot unambiguously distinguish GR from modified gravity [via D=c dz/h(z)]
Reproducing the expansion history with effective w(a) Flat DGP expansion history is very close to GR + Dark Energy with
Minimal Modified Gravity However, gravity theory affects the growth rate, so weak lensing can distinguish GR from modified gravity in principle. A convenient parametrisation for the growth rate is (Linder 2005) γ 0.55 (GR) γ 0.68 (flat DGP) Main question: is there any evidence that γ deviates from GR value? Bayesian approach compute B = p(model 1 data)/p(model 2 data) regardless of the values of the parameters in the models ( evidence ratio )
Prospects Compare GR with Dark Energy with a modified gravity model with the same expansion history. Compute Expected Bayesian evidence: ~ do the data require a modification to GR? Pan-STARRS 1 + Planck+BAO+SNe: Euclid + Planck + BAO + SNe: lnb =3.8 (DGP/GR) lnb =63 (DGP/GR) Euclid should be able to find evidence for gravity theory beyond GR, if it is there. Planck + Euclid!')(!') " "!'#(!'#!#! # $ % &!! WMAP +WL (now) Planck Planck+Euclid Daniel et al 2009 Heavens et al 2007 DGP Caveat: nonlinear clustering in non-gr