Gravitational Lensing and the Dark Energy 1 -0.9 0.5 ' w -1 w 0 -0.5 -1.1 Future Prospects -1 0.6 0.65 0.7 0.6 0.65 0.7 ΩDE Wayne Hu ΩDE SLAC, August 2002 Outline • Standard model of cosmology • Gravitational lensing • Lensing probes of dark energy Outline • Standard model of cosmology • Gravitational lensing • Lensing probes of dark energy Collaborators • Charles Keeton • Takemi Okamoto • Max Tegmark • Martin White Outline • Standard model of cosmology • Gravitational lensing • Lensing probes of dark energy Collaborators • Charles Keeton • Takemi Okamoto • Max Tegmark • Martin White Microsoft http://background.uchicago.edu ("Presentations" in PDF) Dark Energy and the Standard Model of Cosmology If its not dark, it doesn't matter! • Cosmic matter-energy budget: Dark Energy Visible Matter Dark Matter Dark Neutrinos Dark Baryons Making Light of the Dark Side • Visible structures and the processes that form them are our only cosmological probe of the dark components • In the standard, well-verified, cosmological model, structures grow through gravitational instability from small-fluctuations (perhaps formed during inflation) 15 Gyr CMB: high redshift anchor IAB 100 Sask Viper TOCO 80 BAM BOOM RINGVSA K) µ 60 ( CAT QMAP Maxima T MAX ∆ SP MSAM Ten OVRO 40 FIRS DASI CBI ATCA ARGOIAC SuZIE BOOM WD BIMA BOOM 20 COBE Pyth W. Hu 5/02 10 100 1000 l Power Spectra of Maps •Original 64º •Band Filtered Photon-Baryon Plasma • Before z~1000 when the CMB was T>3000K, hydrogen ionized • Free electrons act as "glue" between photons and baryons by Compton scattering and Coulomb interactions • Nearly perfect fluid Peak Location •Fundmentalphysicalscale, the distance sound travels, becomes an angular scale by simple projection according to the angular diameterdistanceDA θA=λA/DA `A=kADA Peak Location •Fundmentalphysicalscale, the distance sound travels, becomes an angular scale by simple projection according to the angular diameterdistanceDA θA=λA/DA `A=kADA •Inaflatuniverse,thedistanceissimplyD = ≡η −η ≈η ,the √ A D 0 ∗ 0 horizon distance, and kA = π/s∗ = 3π/η∗ so η∗ θA ≈ η0 Peak Location •Fundmentalphysicalscale, the distance sound travels, becomes an angular scale by simple projection according to the angular diameterdistanceDA θA=λA/DA `A=kADA •Inaflatuniverse,thedistanceissimplyD = ≡η −η ≈η ,the √ A D 0 ∗ 0 horizon distance, and kA = π/s∗ = 3π/η∗ so η∗ θA ≈ η0 1/2 ◦ • In a matter-dominated universe η ∝ a so θA ≈ 1/30 ≈ 2 or `A ≈ 200 Angular Diameter Distance Test 80 l1~200 60 K) m ( T D 40 20 Boom98 CBI Maxima-1 DASI 500 1000 1500 l (multipole) Curvature • In a curved universe, the apparent or angular diameter distance is nolongertheconformaldistanceDA=Rsin(D/R)6=D α DA D=Rθ λ • Objects in a closed universe are further than they appear! gravitational lensing of the background... Curvature in the Power Spectrum •Angular location of harmonic peaks •Flat = critical density = missing dark energy Accelerated Expansion from SNe • Missing energy must also accelerate the expansion at low redshift High-Z SN Search Team 44 Supernova Cosmology Project 42 ) g 40 a m ( 38 M Ω Ω - m=0.3, Λ=0.7 m 36 Ωm=0.3, ΩΛ=0.0 34 Ωm=1.0, ΩΛ=0.0 ) 1.0 g a m ( 0.5 ) M - 0.0 m ( ∆ -0.5 -1.0 0.01 0.10 1.00 compilation from High-z team z Acceleration Implies Negative Pressure • Role of pressure in the background cosmology • Homogeneous Einstein equations Gµν = 8πGTµν imply the two Friedman equations (flat universe, or associating curvature 2 ρK = −3K/8πGa ) 1 da2 8πG = ρ a dt 3 1 d2a 4πG = − (ρ + 3p) a dt2 3 so that the total equation of state w ≡ p/ρ < −1/3 for acceleration Acceleration Implies Negative Pressure • Role of pressure in the background cosmology • Homogeneous Einstein equations Gµν = 8πGTµν imply the two Friedman equations (flat universe, or associating curvature 2 ρK = −3K/8πGa ) 1 da2 8πG = ρ a dt 3 1 d2a 4πG = − (ρ + 3p) a dt2 3 so that the total equation of state w ≡ p/ρ < −1/3 for acceleration µ • Conservation equation ∇ Tµν = 0 implies ρ˙ a˙ = −3(1 + w) ρ a • so that ρ must scale more slowly than a−2 Dark Mystery? • Coincidence: given different scalings with a, why are dark matter and energy densities comparable now? 1 radiation 0.8 Ω 0.6 matter 0.4 dark energy fraction of critical 0.2 w=-1/3 w=-1 10-5 10-4 10-3 10-2 10-1 scale factor a Dark Mystery? • Coincidence: given different scalings with a, why are dark matter and energy densities comparable now? • Stability: why doesn't negative pressure imply accelerated collapse? or why doesn't the vacuum suck? Gravity Pressure Dark Mystery? • Coincidence: given different scalings with a, why are dark matter and energy densities comparable now? • Stability: why doesn't negative pressure imply accelerated collapse? or why doesn't the vacuum suck? pressure gradients, not pressure, establish stability Dark Mystery? • Coincidence: given different scalings with a, why are dark matter and energy densities comparable now? • Stability: why doesn't negative pressure imply accelerated collapse? or why doesn't the vacuum suck? pressure gradients, not pressure, establish stability • Candidates: Cosmological constant w=-1, constant in space and time, but >60 orders of magnitude off vacuum energy prediction Ultralight scalar field, slowly rolling in a potential, 2 Klein-Gordon equation: sound speed cs =δp/δρ=1 Tangled defects w=-1/3, -2/3 but relativistic sound speed ("solid" dark matter) Dark Energy Probes • (Comoving) distance-redshift relation: a = (1 + z)−1 Z 1 1 Z z 1 D = da 2 = dz a a H(a) 0 H(a) 8πG H2(a) = (ρ + ρ ) 3 m DE in a flat universe, e.g. angular diameter distance, luminosity distance, number counts (volume)... Dark Energy Probes • (Comoving) distance-redshift relation: a = (1 + z)−1 Z 1 1 Z z 1 D = da 2 = dz a a H(a) 0 H(a) 8πG H2(a) = (ρ + ρ ) 3 m DE in a flat universe, e.g. angular diameter distance, luminosity distance, number counts (volume)... • Pressure growth suppression: δ ≡ δρm/ρm ∝ aφ d2φ 5 3 dφ 3 + − w(z)Ω (z) + [1 − w(z)]Ω (z)φ = 0 , d ln a2 2 2 DE d ln a 2 DE where w ≡ pDE/ρDE and ΩDE ≡ ρDE/(ρm + ρDE) e.g. galaxy cluster abundance, gravitational lensing... Large-Scale Structure and Gravitational Lensing Making Light of the Dark Side • Visible structures and the processes that form them are our only cosmological probe of the dark components • In the standard, well-verified, cosmological model, structures grow through gravitational instability from small-fluctuations (perhaps formed during inflation) 15 Gyr Structure Formation Simulation • Simulation (by A. Kravstov) Galaxy Power Spectrum Data Galaxy clustering tracks the dark matter – but bias depends on type • 105 2dF PSCz <1994 3 104 Mpc) -1 h ) ( k ( P 103 0.01 0.1 1 k (h Mpc-1) A Fundamental Problem • All cosmological observables relate to the luminous matter: photon-baryon plasma, galaxies, clusters of galaxies, supernovae • Implications for the dark energy or cosmology in general depend on modelling the formation and evolution of luminous objects • Success of CMB anisotropy is in large part based on the solid theoretical grounding of its formation and evolution – well understood linear gravitational physics A Fundamental Problem • All cosmological observables relate to the luminous matter: photon-baryon plasma, galaxies, clusters of galaxies, supernovae • Implications for the dark energy or cosmology in general depend on modelling the formation and evolution of luminous objects • Success of CMB anisotropy is in large part based on the solid theoretical grounding of its formation and evolution – well understood linear gravitational physics • Distortion of the images of luminous objects by gravitational lensing is equally well understood • Problem: image distortion is typically at %-level – very demanding for the control of systematic errors – but recall CMB is 10-5level!(Tyson,Wenk&Valdes1990) Example of Weak Lensing • Toy example of lensing of the CMB primary anisotropies • Shearing of the image Lensing Observables • Image distortion described by Jacobian matrix of the remapping 1 − κ − γ1 −γ2 A = , −γ2 1 − κ + γ1 where κ is the convergence, γ1, γ2 are the shear components Lensing Observables • Image distortion described by Jacobian matrix of the remapping 1 − κ − γ1 −γ2 A = , −γ2 1 − κ + γ1 where κ is the convergence, γ1, γ2 are the shear components • related to the gravitational potential Φ by spatial derivatives z Z s dD D(Ds − D) ψij(zs) = 2 dz Φ,ij , 0 dz Ds ψij = δij − Aij, i.e. via Poisson equation Z zs 3 2 dD D(Ds − D) κ(zs) = H0 Ωm dz δ/a , 2 0 dz Ds Gravitational Lensing by LSS • Shearing of galaxy images reliably detected in clusters • Main systematic effects are instrumental rather than astrophysical Cluster (Strong) Lensing: 0024+1654 Colley, Turner, & Tyson (1996) Instrumental Systematics • Raw data has instrumental systematics (PSF anisotropy) larger than signal, removed by demanding stars be round Jarvis et al. (2002) 1% ellipticity Instrumental Systematics • Raw data has instrumental systematics (PSF anisotropy) larger than signal, removed by demanding stars be round Jarvis et al. (2002) 1% ellipticity Cosmic Shear Data • Shear variance as a function of smoothing scale compilation from Bacon et al (2002) Shear Power Modes • Alignment of shear and wavevector defines modes ε β Shear Power Spectrum • Lensing weighted Limber projection of density power spectrum • ε−shear power = κ power –4 10 Non-linear k=0.02 h/Mpc zs Linear π 10–5 /2 εε l C +1) l –6 ( 10 l Limber approximation 10–7 zs=1 10 100 1000 Kaiser (1992) l Jain & Seljak (1997) Hu (2000) PM Simulations • Simulating mass distribution is a routine exercise Convergence