Physics of the Large Scale Structure Pengjie Zhang
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1 Physics of the Large Scale Structure Pengjie Zhang Department of Astronomy Shanghai Jiao Tong University The observed galaxy distribution of the nearby universe 0.7 billion lys Observer The observed galaxy distribution of the nearby universe SDSS redshift survey Sloan great wall 1.4 billion lys CfA2 redshift survey CfA2 great wall The observed galaxy distribution of the nearby universe Cosmic web can be described statistically 4 billion lys SDSS redshift survey What is the large scale structure? Large scale structure Intrinsic inhomogeneities Not illusion of observation beyond randomness Not fluke of randomness At >~ Mpc scale Not internal structure of galaxies Not distribution at specific region (since we do not know the initial condition) Ensemble average > volume average The large scale structure of the universe Fundamental physics Precision modeling Precision measurement Galaxy clusteringweak LSS lensingclusters, void, SZ, ISW, peculiar velocities, etc. Dark Baryons matter The large scale structure of the universe Part 1: • Deciphering the large scale structure (LSS) • With statistics and physics Part 2: • Tracers of LSS • Broadband power spectrum, BAO, redshift distortion, weak lensing, SZ effect, etc. Part 3 • Synergies of LSS tracers • Probe DM, DE, MG, neutrino, etc. • Reduce statistical errors • Control systematic errors How to describe the large scale structure? With statistics! N-point correlation functions and their Fourier transforms – 2-point correlation– power spectrum N-point joint PDF Peak analysis Topological descriptions: Minkowski functionals (and genus in particular), etc. Twopoint correlation function 3 3 P12 =(¯n1d x1)(¯n2d x2)[1+ξ(r)] x 2 P12: pairs of galaxies Correlation function.: r what beyond average. Depends on the pair x1 separation vector r. In real measurement, we have to eliminate observational effect Correlation function: correlated feild 3 3 P12 =(¯n1d x1)(¯n2d x2)[1+ξ(r)] n(x) −n The overdensity δ(x) ≡ field n ξ(r) ≡δ(x)δ(x + r)x The observed galaxy correlation function Smaller scale measurement: Larger scale measurement: requires high number denisty requires large volume ξ(r) The z=0 correlation function: • a featureless power-law • Correlation length: ~5 Mpc/h 1 Nonlinear Linear regime r 1 10 100 Mpc/h Features in the galaxy correlation function r ∼−1.8 ξ(r) r0 ξ(r) 1 Bump at 100 Mpc/h eg. Zehavi+, 2004 eg. Eisenstein+, 2005 r 1 10 100 Type dependence. Deviation from power-law eg. Zehavi+, 2004 eg. Zehavi+, 2003 Closer look at the correlation function x2 r 3 3 P12 =(¯n1d x1)(¯n2d x2)[1+ξ(r)] x1 3 3 P12(x1,x2)=(¯n1d x1)(¯nd x2)[1 + ξ(r ≡ x2 − x1,x1)] Our universe should be homogeneous ξ(r ≡ x2 − x1,x1) → ξ(r ≡ x2 − x1) Our universe should be isotropic ξ(r ≡ x2 − x1) → ξ(r) More features: anisotropies Line of sight ξ(r)=ξ(σ, π) x r 2 π σ x1 Observer e.g. Peacock+, 2001, with 141,000 2dF galaxies More features: anisotropies ξ(r)=ξ(σ, π) e.g. Peacock+, 2001, with 141,000 2dF galaxies 2010+: larger scale coverage, higher accuracy e.g. Li+, 2016, with 0.5M BOSS galaxies Some anisotropies are so prominent that we can simply see by eyes in 1980s! Observer Correlation function –> Power spectrum n(x) −n δ(x) ≡ n δ(k) ≡ d3xδ(x)eik·x homogeneity 3 δ(k)δ(k ) =(2π) δ3D(k + k )P (k) P (k)= d3rξ(r)eik·r Rich features in the power spectrum Tegmark Rich features in the power spectrum P (k) ≡ P (|k)|) P (k) 5.0 0.4 4.5 0.2 0.0 4.0 [h/Mpc] || k −0.2 3.5 −0.4 3.0 −0.4 −0.2 0.0 0.2 0.4 k [h/Mpc] ⊥ DR11 e.g. Li+ 2016 Even more features: “abnormal” correlation at horizon scales 0.04 17 < g < 19 19 < g < 19.5 0.02 Separate by ~3000 Mpc/h 0.00 -0.02 0.04 19.5 < g < 20 20 < g < 20.5 ) θ ( 0.02 GQ w 0.00 dN/dz -0.02 0.01 0.1 1 0.04 20.5 < g < 21 θ (degrees) 0.02 0.00 -0.02 0.01 0.1 1 0 0.5 1 z 1.5 2 θ (degrees) Fig. 1.— Galaxy redshift distribution from applying our 17 < r<21 magnitude limit to the CNOC2 luminosity function and quasar redshift distribution inferred from quasar photometric red- shifts (solid lines). The fitted redshift distributions from Equa- Non-vanishing correlation! tion 8 are shown with dashed lines. In all cases, the amplitude scaling is arbitrary. First detected by Scranton+, 2005 at ~10sigma and then by other data Even more features: “abnormal” correlation at horizon scales Galaxies at z~1 CMB at z~1100 Separate by ~6000 Mpc/h Non-vanishing correlation detected at ~4sigma, by NVSS/SDSS/WISE +WMAP/Planck Understanding LSS with physics Initial conditions set at early time Evolution under laws of physics LSS we observe at late time Understanding LSS with physics Initial fluctuations Fluctuations at z ∼ 100 Linear perturbation P (k) ∝ k0.96 at k → 0 0.96 Boltzmann equation P (k) ∝ k P (k) ∝ k0.96−4 at k →∞ • High order perturbation theory • Halo model, Effective field theory of LSS • N-body simulations • Hydrodynamic simulations • Semi-analytical models • Halo occupation distribution, Conditional luminosity function Movies of simulation: The Millennium The Elucid project Complexities to understand LSS Task: evolve the universe from z~100 to z~0 Complexities – Dark matter, baryons, photons, neutrinos, dark energy – Gravity: nonlinear evolution at ~10 Mpc/h under gravity GR effect at >~103 Mpc/h – Non-gravitational forces: gastrophysics, galaxy formation and feedback – Mapping underlying matter/energy into observable signals (galaxy distribution, galaxies shapes, secondary CMB, etc.) – Eliminating observational contaminations in the desired cosmological signals An example of simplified treatment Set neutrinos=0, photons=0. Neglect gastrophysics of baryons. Then only gravity. Baryons behave the same as DM Assume smooth dark energy. Then DE only affects the expansion. Assume DE=Lambda Assume flatness The universe to evolve Dark matter (=DM+baryons), Lambda Flat gravity Two steps Step 1: evolution of the dark matter field – Large scales: linear perturbation (GR effect can be included too) – Intermediate scales: spherical collapse – Small scales (and actually all scales): N-body simulations Step 2: identify virialized regions (dark matter halos) and put galaxies in – Halo mass function, halo bias/spatial clustering – Halo occupation distribution/Conditional luminosity function (the number of galaxies as a function of halo mass) Step 1linear evolution Gμν() gμν = μν T Nonlinear entialdiffer equation FRW gμν= gμν + μν h Perturb oundar the oundbackgr G 2G FRW ∂ μν 1 ∂ μν Gμν()μ gν + hαβ = Tμν − 2 hαβ χδ h + ∂gαβ ∂gαβ ∂ gχδ Neglect high order perturbation terms ds2 = −(1 + 2ψ)dt2 + a2(1 + 2φ) dxi,2 i Tμν = ρUμUν (P ) =0 ρ =¯ρ(1 + δ) Step 1linear evolution: Lambda: sub-horizon 2 2 −3 H (a)=H0 (Ωma +ΩΛ) d2δ dδ dH/da 3 3 H2Ω δ + + − 0 m =0 da2 da H a 2 H2a3 a2 Linear growth factor a da δ(x, a) ∝ H δ(x, a =0) 3 3 Heath 1977 0 H a Carroll, Press & Turner (1992) From sub-horizon to super-horizon 2 2 2 0 2 ðr þ 3KÞ À 3a H ð a þ Þ¼4G ma m; GR effect 0 2 aHð a þ Þ¼4G ma W; r2W 0 ¼ þ 30: m a2H GR effect Z a ~ / da ½1 þ ð Þ m H 3 3 C k; a : 0 H a 3 2 2 0 1 3 2 ð Þ¼ a H H a þ R =H a C k;a 2 a 3 3 k H 0 da=H a 2ð Þ2 0 1 3 2 ¼ a H=H0 H a þ R =H a 3 À1 2 a 3 3 : 3ðk  10 h MpcÞ H 0 da=H a ZPJ 2011 From linear to nonlinear scales Halo model, halofit, EFT, etc. high order ptsimulations Linear Nonlinear N-body z=0 simulations today non-linear 10-104 Mpc/h k3P (k) evolution z=1 2 109-12particles Δ (k) ≡ z=2 2π2 2-4 linear z=3 ~10 cpus growth z=4 z=5 days-months Credit: Percival’s lectures Can it explain the observed galaxy clustering? Some but not all! r ∼−1.8 ξ(r) r0 ξ(r) 1 Bump at 100 Mpc/h eg. Zehavi+, 2004 eg. Eisenstein+, 2005 r 1 10 100 Type dependence. Deviation from power-law eg. Zehavi+, 2004 eg. Zehavi+, 2003 The power-law correlation at ~1 Mpc/h k3P (k) 1 ∼−1.8 Δ2(k) ≡ ∼ ξ r ∼ ⇒ ξ(r) ∼ r 2π2 k z=0 non-linear r ∼−1 ξ(r) evolution z=1 r0 z=2 linear z=3 growth z=4 z=5 eg. Zehavi+, 2004 Deviation from power-law eg. Zehavi+, 2003 What about the bump at ~100 Mpc/h? Baryon acoustic oscillations Sound horizon cat decoupling c √ s 3 varying the baryon fraction Bump at 100 Mpc/h eg. Eisenstein+, 2005 A missing ingredient Type dependence. eg. Zehavi+, 2004 Larger DM halos More/larger galaxies Smaller DM halos Less/smaller galaxies Bias 2 ξhalo = b (M)ξDM Type dependence. eg. Zehavi+, 2004 Jing 1998 Rich cosmological information Large scale small scale GR effect BAO, RSD-> DE, gravity z=0 PNG non-linear evolution z=1 z=2 linear z=3 growth z=4 z=5 Neutrinos, DM Cosmic magnification (weak lensing).