Probing the Dark Side. of Structure Formation Wayne Hu

Transcription

1 Probing the Dark Side 1 SDSS 100 MAP Planck P(k) 10 3 T LSS Pψ CMB l (multipole) 0.01 k (h Mpc -1 ) Lensing l (multipole) of Structure Formation Wayne Hu

2 The Dark Side of Structure Formation The Dark Side All components that contributes to the expansion rate that do not couple to ordinary matter at the present

3 The Dark Side of Structure Formation The Dark Side All components that contributes to the expansion rate that do not couple to ordinary matter at the present The Usual Suspects Cold dark matter, dark baryons, cosmological constant, spatial curvature Establishing the basic cosmological framework at high redshifts through sub degree scale CMB anisotropies Achieving precision with large-scale structure from galaxy surveys, lensing... Constructing consistency tests between these measures, distance measures...

4 The Dark Side of Structure Formation The Dark Side All components that contributes to the expansion rate that do not couple to ordinary matter at the present The Usual Suspects Cold dark matter, dark baryons, cosmological constant, spatial curvature Establishing the basic cosmological framework at high redshifts through sub degree scale CMB anisotropies Achieving precision with large-scale structure from galaxy surveys, lensing... Constructing consistency tests between these measures, distance measures... Other Shady Characters Massive neutrinos, scalar fields, decaying dark matter, background neutrinos... Observationally testing the properties of the dark sector combining low and high redshift information

5 Collaborators Past & Present Microwave Background Emory Bunn Asantha Cooray Andrei Gruzinov Douglas Scott Uros Seljak Joe Silk Naoshi Sugiyama Martin White Matias Zaldarriaga Large-Scale Structure Rupert Croft Romeel Dave Daniel Eisenstein Jim Peebles Alex Szalay Max Tegmark

6 Collaborators Past & Present Microwave Background Emory Bunn Asantha Cooray Andrei Gruzinov Douglas Scott Uros Seljak Joe Silk Naoshi Sugiyama Martin White Matias Zaldarriaga Large-Scale Structure Rupert Croft Romeel Dave Daniel Eisenstein Jim Peebles Alex Szalay Max Tegmark Presentation Microsoft

7 Part I: Establishing the Cosmological Framework Begin with the CMB because... Linearity observed: T/T ~ 10 5 Simple Physics Gravity Fluid Dynamics Geometry Rich Features Acoustic Peaks

8 CMB Anisotropies Tegmark, de Oliviera Costa, Devlin, Netterfield, & Page (1996)

9 Current CMB Quilt 10 1 θ (degrees) T (µk) W. Hu Nov l (multipole) COBE PythV-95 IAC TOCO97/98 Sask MSAM CAT QMAP MAX Tene SP94 Argo MSAM Viper RING ATCA FIRS BAM SP91Pyth IAB MSAM WD OVRO SuZIE

10 Projected MAP Errors 10 1 θ (degrees) T (µk) W. Hu Feb l (multipole)

11 Projected Planck Errors 10 1 θ (degrees) T (µk) W. Hu Feb l (multipole)

12 z > 1000; T γ > 3000K Hydrogen ionized Free electrons glue photons to baryons γ e p compton scattering coulomb interactions Photon baryon fluid Potential wells that later form structure Thermal History tightly coupled fluid cold hot mean free path << wavelength hot

13 Thermal History z > 1000; T γ > 3000K Hydrogen ionized Free electrons glue photons to baryons γ e p compton scattering coulomb interactions Photon baryon fluid Potential wells that later form structure z ~ 1000; T γ ~ 3000K Recombination Fluid breakdown z < 1000; T γ < 3000K Gravitational redshifts & lensing Reionization; rescattering last scattering λ k -1 surface z=1000 θ l -1 recombination observer

14 Angular Diameter Distance Spatial Curvature Standardized ruler Measure angular extent Ruler & comoving distance scale (except for Λ) Infer curvature Robust Physical Scales Sound horizon Peak spacing Diffusion scale Damping tail Flat Power 1 Closed 0.1 Kamionkowski, Spergel & Sugiyama (1994) Hu & White (1996) l

15 Curvature and the Cosmological Constant Ω K 0 Shifted Acoustic Signature Power Ω Λ 0 W. Hu 2/ l Gravitational Redshift 0.9 Power l

16 The Acoustic Peaks Acoustic Oscillations Peak Positions Baryon Drag Radiation Driving Diffusion Damping

17 Photon pressure resists compression in potential wells Acoustic oscillations Acoustic Oscillations Photon Pressure Effective Mass Peebles & Yu (1970) Potential Well Ψ Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)

18 Acoustic Oscillations Photon pressure resists compression in potential wells Acoustic oscillations Gravity displaces zero point Θ δt/t = Ψ Oscillation amplitude = initial displacement from zero pt. Θ (-Ψ) = 1/3Ψ T/T Θ+Ψ η initial displ. zero point Ψ /3 Peebles & Yu (1970) Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)

19 Acoustic Oscillations Photon pressure resists compression in potential wells Acoustic oscillations Gravity displaces zero point Θ δt/t = Ψ Oscillation amplitude = initial displacement from zero pt. Θ (-Ψ) = 1/3Ψ Gravitational redshift: observed (δt/t) obs = Θ +Ψ oscillates around zero T/T Θ+Ψ First Extrema η Ψ /3 Peebles & Yu (1970) Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)

20 Acoustic Oscillations Photon pressure resists compression in potential wells Acoustic oscillations Gravity displaces zero point Θ δt/t = Ψ Oscillation amplitude = initial displacement from zero pt. Θ (-Ψ) = 1/3Ψ Gravitational redshift: observed (δt/t) obs = Θ +Ψ oscillates around zero T/T Θ+Ψ Second Extrema η Ψ /3 Peebles & Yu (1970) Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)

21 Harmonic Peaks Oscillations frozen at last scattering Wavenumbers at extrema = peaks Sound speed c s T/T Θ+Ψ Last Scattering First Peak Ψ /3 k 1 =π/ sound horizon η Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)

22 Harmonic Peaks Oscillations frozen at last scattering Wavenumbers at extrema = peaks Sound speed c s T/T Θ+Ψ Last Scattering Frequency ω = kc s ; conformal time η last scattering Phase k ; φ = 0 dη ω = k Harmonic series in sound horizon φ n = nπ k n = nπ/ First Peak T/T Θ+Ψ sound horizon Last Scattering sound horizon η η Ψ /3 k 1 =π/ sound horizon Ψ /3 k 2 =2k 1 Second Peak Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)

23 Baryons provide inertia Relative momentum density R = (ρ b + p b )V b / (ρ γ + p γ )V γ Ω b h2 Effective mass m eff = (1 + R) Baryon Drag T/T zero pt Low Baryon Content Ψ /3 η Hu & Sugiyama (1995)

24 Baryons provide inertia Relative momentum density R = (ρ b + p b )V b / (ρ γ + p γ )V γ Ω b h2 Effective mass m eff = (1 + R) Baryon Drag Baryons drag photons into potential wells zero point Amplitude Frequency (ω m eff 1/2 ).. Constant R, Ψ: (1+ R) Θ + (k 2 /3)Θ = (1+ R) (k 2 /3)Ψ Θ + Ψ = [Θ(0) + (1+ R) Ψ(0)] cos [ kη/ 3 (1+ R)] RΨ Θ+Ψ T/T η zero pt High Baryon Content Ψ /3 Hu & Sugiyama (1995)

25 Baryons provide inertia Relative momentum density R = (ρ b + p b )V b / (ρ γ + p γ )V γ Ω b h2 Effective mass m eff = (1 + R) Baryon Drag Baryons drag photons into potential wells zero point Amplitude Frequency (ω m eff 1/2 ).. Constant R, Ψ: (1+ R) Θ + (k 2 /3)Θ = (1+ R) (k 2 /3)Ψ Θ + Ψ = [Θ(0) + (1+ R) Ψ(0)] cos [ kη/ 3 (1+ R)] RΨ T/T Θ+Ψ zero pt Alternating Peak Heights Ψ /3 η Hu & Sugiyama (1995)

26 Baryons in the CMB Power Baryon Drag Power/Damping Power High odd peaks 500 l 1000 Ω b h Additional Effects Time varying potential Dissipation/Fluid imperfections 0.1 Power W. Hu 2/ l 0.1

27 Driving Effects and Matter/Radiation Potential perturbation: Radiation Potential: k 2 Ψ = 4πGa 2 δρ generated by radiation inside sound horizon δρ/ρ pressure supported δρ hence Ψ decays with expansion Ψ T/T η Θ+Ψ Hu & Sugiyama (1995)

28 Driving Effects and Matter/Radiation Potential perturbation: Radiation Potential: Potential Radiation: Feedback stops at matter domination k 2 Ψ = 4πGa 2 δρ generated by radiation inside sound horizon δρ/ρ pressure supported δρ hence Ψ decays with expansion Ψ decay timed to drive oscillation 2Ψ + (1/3)Ψ = (5/3)Ψ 5x boost Ψ T/T Θ+Ψ η Hu & Sugiyama (1995)

29 Driving Effects and Matter/Radiation Potential perturbation: Radiation Potential: Potential Radiation: Feedback stops at matter domination k 2 Ψ = 4πGa 2 δρ generated by radiation inside sound horizon δρ/ρ pressure supported δρ hence Ψ decays with expansion Ψ decay timed to drive oscillation 2Ψ + (1/3)Ψ = (5/3)Ψ 5x boost Ψ T/T Θ+Ψ η Hu & Sugiyama (1995)

30 Matter Density in the CMB Power Ω m h 2 Power/Damping Amplitude ramp across matter radiation equality Radiation density fixed by CMB temperature & thermal history 5 Power Ω m h Measure Ω m h 2 from peak heights 1 Power W. Hu 2/ l

31 Dissipation / Diffusion Damping Imperfections in the coupled fluid mean free path λ C in the baryons Random walk over diffusion scale: geometric mean of mfp & horizon λ D ~ λ C N ~ λ C η >> λ C Overtake wavelength: λ D ~ λ ; second order in λ C /λ Viscous damping for R<1; heat conduction damping for R>1 N=η / λ C 1.0 λ D ~ λ C N λ Power 0.1 perfect fluid instant decoupling Silk (1968); Hu & Sugiyama (1995); Hu & White (1996) l

32 Dissipation / Diffusion Damping Rapid increase at recombination as mfp Independent of (robust to changes in) perturbation spectrum Robust physical scale for angular diameter distance test (Ω K, Ω Λ ) Recombination 1.0 Power 0.1 perfect fluid instant decoupling recombination Silk (1968); Hu & Sugiyama (1995); Hu & White (1996) l

33 Physical Decomposition & Information 4 combined Power 3 2 temperature doppler l

34 Physical Decomposition & Information Fluid + Gravity alternating peaks photon-baryon ratio Ω b h 2 4 baryon drag Power l

35 Physical Decomposition & Information Fluid + Gravity alternating peaks photon-baryon ratio Ω b h 2 driven oscillations matter radiation ratio Ω m h 2 Power matter radiation equality l

36 Physical Decomposition & Information Fluid + Gravity alternating peaks photon-baryon ratio Ω b h 2 driven oscillations matter radiation ratio Ω m h 2 Fluid Rulers sound horizon damping scale Power πk A k D diffusion damping perfect fluid 500 l

37 Physical Decomposition & Information Fluid + Gravity alternating peaks photon-baryon ratio Ω b h 2 driven oscillations matter radiation ratio Ω m h 2 Fluid Rulers sound horizon damping scale Geometry angular diameter distance f(ω Λ,Ω K ) + flatness or no Ω Λ, Ω Λ or Ω K Power l A =d A πk A ISW 500 l D =d A k D l

38 Cosmological Parameters in the CMB Baryon Photon Ratio Matter Radiation Ratio Ω b h Ω m h l(l+1)cl 10 1 l(l+1)cl l l Curvature 0 Cosmological Constant 0 Ω K 0.5 Ω Λ 0.5 Ω Λ 0.9 l(l+1)cl 0.9 l(l+1)cl W.Hu 2/ l l

39 P(k) T/T k CMB Polarization l LSS +High-z CMB Anisotropy Measurements P(k)? Clustering Properties of Matter k CMB Pol T/T Gravity Waves Vorticity? CMB Polarization l Density Perturbations % Level Classical Cosmological Parameters + Origin of Fluctuations (inflation?) Nature of Dark Matter Bias Cosmological Parameters + Origin and Evolution of Fluctuations (inflation?) Cosmological Model Gravity? LSS + High-z Origin and Evolution of Structure (defects?)

40 Part II: Complementarity: Achieving Precision through Large Scale Structure Acoustic oscillations in the matter power spectrum Isolating classical cosmological parameters Weak lensing by large scale structure Measuring the growth rate of perturbations

41 Acoustic Peaks in the Matter Baryon density & velocity oscillates with CMB Baryons decouple at τ / R ~ 1, the end of Compton drag epoch Decoupling: δ b (drag) V b (drag), but not frozen End of Drag Epoch Hu & Sugiyama (1996)

42 Acoustic Peaks in the Matter Baryon density & velocity oscillates with CMB Baryons decouple at τ / R ~ 1, the end of Compton drag epoch Decoupling: δ b (drag) V b (drag), but not frozen. Continuity: δ b = kv b Velocity Overshoot Dominates: δ b V b (drag) kη >> δ b (drag) Oscillations π/2 out of phase with CMB Infall into potential wells (DC component) End of Drag Epoch Velocity Overshoot + Infall Hu & Sugiyama (1996)

43 Features in the Power Spectrum Features in the linear power spectrum Break at sound horizon Oscillations at small scales; washed out by nonlinearities P(k) (arbitrary norm.) Eisenstein & Hu (1998) numerical nonlinear scale k (h Mpc -1 )

44 Features in the Power Spectrum Features in the linear power spectrum Break at sound horizon Oscillations at small scales; washed out by nonlinearities Peacock & Dodds (1994) P(k) (arbitrary norm.) m v = 0 ev m v = 1 ev nonlinear scale W. Hu Feb k (h Mpc -1 )

45 Features in the Power Spectrum Features in the linear power spectrum Break at sound horizon Oscillations at small scales; washed out by nonlinearities SDSS BRG P(k) (arbitrary norm.) m v = 0 ev m v = 1 ev nonlinear scale W. Hu Feb k (h Mpc -1 )

46 Combining Features in LSS + CMB Consistency check on thermal history and photon baryon ratio Infer physical scale l peak (CMB) k peak (LSS) in Mpc 1 Power (arbitrary norm.) k3p γ (k) ΛCDM 0.05 k (Mpc 1) 0.1 Eisenstein, Hu & Tegmark (1998) Hu, Eisenstein, Tegmark & White (1998)

47 Combining Features in LSS + CMB Consistency check on thermal history and photon baryon ratio Infer physical scale l peak (CMB) k peak (LSS) in Mpc 1 Measure in redshift survey k peak (LSS) in h Mpc 1 h ΛCDM 8 Power (arbitrary norm.) h k3p γ (k) P m (k) 0.05 k (Mpc 1) 0.1 Eisenstein, Hu & Tegmark (1998) Hu, Eisenstein, Tegmark & White (1998)

48 Combining Features in LSS + CMB Consistency check on thermal history and photon baryon ratio Infer physical scale l peak (CMB) k peak (LSS) in Mpc 1 Measure in redshift survey k peak (LSS) in h Mpc 1 h Robust to low redshift physics (e.g. quintessence, GDM) Power (arbitrary norm.) h k3p γ (k) ΛCDM QCDM w g = 1/2 P m (k) 0.05 k (Mpc 1) 0.1 Eisenstein, Hu & Tegmark (1998) Hu, Eisenstein, Tegmark & White (1998)

49 MAP +P +SDSS H 0 ±130 ±23 ±1.2 Ω m ±1.4 ±0.25 ±0.016 CMB: ~line of constant 2 Ω m H 0 Ω m +Ω Λ MAP(P) Ω Λ 0.4 H Classical Cosmology SDSS Eisenstein, Hu, Tegmark (1998) Ω m

50 MAP +P +SDSS H 0 ±130 ±23 ±1.2 Ω m ±1.4 ±0.25 ±0.016 Ω Λ ±1.1 ±0.20 ± Classical Cosmology Any other measurement (including H 0 ) breaks degeneracy 0.2 Ω Λ 0.4 H Eisenstein, Hu, Tegmark (1998) Ω m

51 MAP +P +SDSS H 0 ±130 ±23 ±1.2 Ω m ±1.4 ±0.25 ±0.016 Ω Λ ±1.1 ±0.20 ± Classical Cosmology Many opportunities for consistency checks! (e.g. high-z SNIa) MAP +SNIa MAP +SDSS Complementarity Consistency ΩΛ SNIa 0.4 MAP 0.2 SDSS Eisenstein, Hu, Tegmark (1998) Ω m

52 Gravitational Lensing by LSS Shearing of galaxy images reliably detected in clusters Main systematic effects are instrumental rather than astrophysical Colley, Turner, & Tyson (1996) Cluster (Strong) Lensing:

53 Statistics of Weak Lensing by LSS Efficient PM simulations to build statistics Tiling of hundreds of independent simulations Convergence sources Shear lenses tiling obs. 6 6 FOV; 2' Res.; h 1 Mpc box; h 1 kpc mesh; M White & Hu (1999)

54 Weak Lensing: Power Spectrum Convergence power spectrum Sub-degree scale power from non-linear regime (l ~ >100) Power PD96 shot noise linear White & Hu (1999)

55 Weak Lensing: Power Spectrum Convergence power spectrum Sub-degree scale power from non-linear regime (l ~ >100) Mean power matches density scaling prediction (PD96) Ratio Power PD96 linear shot noise vs PD96 White & Hu (1999)

56 Weak Lensing: Power Spectrum Convergence power spectrum Sub-degree scale power from non-linear regime (l ~ >100) Mean power matches density scaling prediction (PD96) Sample variance near Gaussian until l~1000 Ratio Power PD96 linear shot noise vs PD96 Sampling Errors Gaussian White & Hu (1999)

57 Weak Lensing: Power Spectrum Convergence power spectrum Sub-degree scale power from non-linear regime (l ~ >100) Mean power matches density scaling prediction (PD96) Sample variance near Gaussian until l~1000 Shot noise from intrinsic ellipticities takes over for l ~ >1000 (γ rms =0.4; deg 1 ) Gaussian approximation reasonable for estimation purposes White & Hu (1999) Ratio Sampling Errors Ratio Power vs shot noise 100 PD96 l shot noise 1000 linear vs PD Gaussian

58 Weak Lensing: Power Spectrum & Cosmological Parameters Potentially as precise as the CMB Systematic effects are under control at the sub% level in shear The Good News: Depends on most (8) cosmological parameters

59 Weak Lensing: Power Spectrum & Cosmological Parameters Potentially as precise as the CMB Systematic effects are under control at the sub% level in shear The Good News: Depends on most (8) cosmological parameters The Bad News: Depends on most (8) cosmological parameters Blandford et al. (1991); Miralda-Escude (1991); Kaiser (1992) Degeneracies! Solutions: Large sky coverage Tomography on source distribution Combination with CMB measurements Nongaussianity

60 Weak Lensing: Power Spectrum & Cosmological Parameters Potentially as precise as the CMB Systematic effects are under control at the sub% level in shear The Good News: Depends on most (8) cosmological parameters The Bad News: Depends on most (8) cosmological parameters Degeneracies! Solutions: Large sky coverage Tomography on source distribution Combination with CMB measurements Nongaussianity

61 Weak Lensing: Power Spectrum & Cosmological Parameters Large sky coverage Comparable precision to CMB per area of sky 11D CDM Space σ(ω m h2) σ(ω b h 2 ) σ(m ν ) σ(ω Λ ) σ(ω K ) σ(n s ) σ(lna) σ(z s ) σ(τ) σ(t/s) σ(y p ) WL f sky (0.02) MAP(T) (1) (0.02) Planck(T+P) (1) Hu & Tegmark (1999)

62 Weak Lensing: Power Spectrum & Cosmological Parameters Divide sample by photometric redshifts Cross correlate samples g i (D) ni(d) 3 (a) Galaxy Distribution (b) Lensing Efficiency D Power l Order of magnitude increase in precision, e.g. Ω Λ Hu (1999)

63 Weak Lensing: Power Spectrum & Cosmological Parameters Combine with CMB f sky: Degeneracy breaking even with 1 FOV (acheivable today) 10 (a) Weak Lensing + MAP Ω Λ z s Ω Κ Order of magnitude gains for > 10 FOV Opportunity to probe the detailed nature of dark energy improvement over CMB 1 10 (b) Weak Lensing + Planck m ν Ω Κ z s Ω Λ mν 1 Hu & Tegmark (1999) 1 Θ deg

64 Weak Lensing: Skewness Skewness of the convergence Sensitive to Ω m, Ω G (Bernardeau et al. 1997, Hui 1999; Jain, Seljak & White 1999) But depends on: degree of non-linearity shape of power spectrum Hierarchical scaling ansatz only applies on deeplynonlinear, shot noise limited scales (<1') Severely limited by sample variance (>1') S 3 PDF σ=10' scaling σ=5' convergence ratio bias White & Hu (1999) σ (arcmin)

65 P(k) T/T k CMB Polarization l LSS +High-z CMB Anisotropy Measurements P(k)? Clustering Properties of Matter k CMB Pol T/T Gravity Waves Vorticity? CMB Polarization l Density Perturbations % Level Classical Cosmological Parameters + Origin of Fluctuations (inflation?) Nature of Dark Matter Bias Cosmological Parameters + Origin and Evolution of Fluctuations (inflation?) Cosmological Model Gravity? LSS + High-z Origin and Evolution of Structure (defects?)

66 Part III: Determining the Properties of the Dark Sector Inconsistent precision measures? Generalized dark matter Examples: massive neutrinos, scalar fields, decaying dark matter, neutrino background radiation

67 Inconsistent Precision Measures? Expect precision results from CMB, galaxy surveys, SNIa, weak lensing... May turn out inconsistent with even the large adiabatic CDM parameter space (11 15 parameters)

68 Inconsistent Precision Measures? Expect precision results from CMB, galaxy surveys, SNIa, weak lensing... May turn out inconsistent with even the large adiabatic CDM parameter space (11 15 parameters) What If CMB shows sub degree scale structure, but not necessarily the peaks of adiabatic CDM Nature of the initial fluctuations isocurvature vs. adiabatic inflation vs. ordinary causal mechanisms Clustering properties of matter scale & time dependent bias gravity on large scales dark matter properties

69 Beyond Cold Dark Matter Parameter estimation and likelihood analysis is only as good as the model space considered Even if we do live in CDM space one should observationally prove dark matter is CDM and missing energy is Λ or scalar field quintessence Need to parameterize the possibilities continuously from CDM to more exotic possibilities Generalized Dark Matter An extention of X-matter (Chiba, Sugiyama & Nakamura 1997) based on gauge invariant variables (Kodama & Sasaki 1984)

70 Generalized Dark Matter Arbitrary Stress Energy Tensor T µν Local Lorentz Invariance Symmetric T µν 16 Components 10 Components Hu (1998)

71 Generalized Dark Matter Arbitrary Stress Energy Tensor T µν 16 Components Local Lorentz Invariance Symmetric T µν 10 Components Energy Momentum Conservation 4 Constraints 1 Pressure 5 Anisotropic stresses Hu (1998)

72 Generalized Dark Matter Arbitrary Stress Energy Tensor T µν Local Lorentz Invariance Symmetric T µν 16 Components 10 Components Energy Momentum Conservation 4 Constraints 1 Pressure 5 Anisotropic stresses Linear Perturbations scalar, vector, tensor 1 Pressure (scalar) 1 Scalar anisotropic stress 2 vorticities 2 Vector anisotropic stress 2 gravity wave pol. 2 Tensor anisotropic stress Homogeneity & Isotropy + Gravitational Instability 1 Background pressure 1 Pressure fluctuation 1 Scalar anisotropic stress fluctuation Hu (1998)

73 Generalized Dark Matter Arbitrary Stress Energy Tensor T µν Local Lorentz Invariance Symmetric T µν 16 Components 10 Components Energy Momentum Conservation 4 Constraints 1 Pressure 5 Anisotropic stresses Linear Perturbations scalar, vector, tensor 1 Pressure (scalar) 1 Scalar anisotropic stress 2 vorticities 2 Vector anisotropic stress 2 gravity wave pol. 2 Tensor anisotropic stress Homogeneity & Isotropy + Gravitational Instability 1 Background pressure 1 Pressure fluctuation 1 Scalar anisotropic stress fluctuation Model as Equations of State Gauge Invariance w =p/ρ 1 Equation of State Hu (1998) c eff 2 =(δp/δρ) comov c vis 2 = (viscosity coefficient) 1 Sound Speed 1 Anisotropic Stress

74 Dark Components equation of state w g sound speed c eff 2 viscosity c vis 2 Prototypes: Cold dark matter (WIMPs) Hot dark matter 1/3 0 (light neutrinos) Cosmological constant 1 arbitrary arbitrary (vacuum energy)

75 Dark Components equation of state w g sound speed c eff 2 viscosity c vis 2 Prototypes: Cold dark matter (WIMPs) Hot dark matter 1/3 0 (light neutrinos) Cosmological constant 1 arbitrary arbitrary (vacuum energy) Exotica: Quintessence variable 1 0 (slowly-rolling scalar field) Decaying dark matter 1/3 0 1/3 (massive neutrinos) Radiation backgrounds 1/3 1/3 0 1/3 (rapidly-rolling scalar field, NBR)

76 Exotic Dark Matter: Examples Two examples (1) Dark Energy (accelerating component) (2) Relativistic Dark Matter (a) alternate model for the seeds of fluctuations (b) neutrino background radiation (number, anisotropies?)

77 Determining the Accelerating Component Is a cosmological constant responsible for the acceleration? σ(w g )=0.13 σ(w g )=0.13 σ(w g )=0.03 σ(w g )=0.03 (MAP+SDSS) (MAP+SN Ia) (Planck+SDSS) (Planck+SN Ia) 0 MAP (P) SDSS If not ( 1<w g <0), is a scalar field responsible? wg sound speed constrained if w g > 1/2 Hu, Eisenstein, Tegmark & White (1998) Consistency Complemetarity MAP + SDSS SNIa MAP SNIa Ωg

78 Relativistic Dark Matter: Model Defining Elements: Additional species of dark matter: relativistic ideal fluid ρ y Scale-invariant isocurvature fluctuations δρ y = (δρ γ + δρ ν + δρ c ) ; k 3 P y (k) = const. Adiabatic relation in the usual components: δ γ = δ ν = 4δ c /3 Phenomenological Consequences: Scale invariant series of 1 Acoustic Peaks 0 Correct CMB/LSS power 1 2 ( T/T = Φ/3) 3 (a) Perfect Fluid Early Universe Pedigree: 2 δ c 1 Scalar field rapidly 0 rolling in quartic potential 1 Gravitationally produced during inflation 2 (b) Massless Particles a ( 10 5 ) amplitude δ δ δ γ y /f c δ y /f δ γ 3 4 Hu & Peebles (1999)

79 Relativistic Dark Matter: Consequences Differs from ΛCDM by ~10% to l= set A Approximate χ2/ν Model All A B ΛCDM Peak heights opposite to ΛCDM for Ω b h 2 for Ω m h 2 Large scale structure sensitive to rel. dark matter dynamics: c 2 vis = 0 vs 1/3 Hu & Peebles (1999) P(k) T (µk) σ 8 = 0.84; 0.86 (Ω m =0.35; h=0.8) Ω b h 2 =0.012 Ω b h 2 =0.02 Massless Particles (Ω b h 2 =0.012) 0.01 l k (h Mpc 1 ) 0.1

80 Detecting the Neutrino Background Radiation Neutrino number N ν or temperature T ν alters the matter radiation ratio Nν MAP no pol pol Degenerate with matter density Ω m h 2 Break degeneracy with NBR anisotropies 5 SDSS Ignoring Anisotropies Ω m h 2 ρ m /ρr fixed MAP+SDSS Hu, Eisenstein, Tegmark & White (1998)

81 Anisotropies in the Neutrino Background Radiation Neutrino quadrupole anisotropies alter Ψ and drive acoustic oscillations Anisotropies well modeled by GDM viscosity c vis 2 =1/3 but largely degenerate Detectability: 1σ, MAP (pol); 3.5σ, MAP+SDSS; 7.2σ, Planck (pol); 8.7σ, Planck+SDSS Power Neutrinos GDM c vis 2 = 1/3 GDM c vis 2 = 0 Hu (1998) Hu, Eisenstein, Tegmark & White (1998) l Nν Nν Ω m h 2 MAP no pol pol SDSS Ignoring Anisotropies SDSS ρ m /ρr fixed MAP+SDSS Employing Anisotropies

82 Einstein Equations G µν =8πGT µν Vector Perturbations FRW Background + Linear Perturbations Tensor Perturbations Stress Free Anisotropic Stress H (±1) >> (p/ρ cr )Π (±1) H (±1) < ~ (p/ρ cr )Π (±1) Stress Free Anisotropic Stress H (±2) T >> (p/ρcr )Π (±2) H (±2) < T ~ (p/ρ cr )Π (±2) Scalar Perturbations Pure Decay Decay from arbitrary initial conditions Stress Integral Defects Scalar Stress ζ S, S Π < ~ Free Gravity Waves tcdm (matter) Stress Integral tcdm (radiation) Defects Clustered 2 Component w 1,w 2 Stress Free ζ >> S, S Π Hu & Eisenstein (1998) Smooth ζ = const. ζ = backgrd. Φ = backgrd. ODE integral Φ = backgrd. ODE All Adiabatic Models except OCDM 2,3 Component w C = w 1 w S = w 1,w 2 ΛCDM OCDM HCDM strcdm φcdm QCDM GDM φqcdm ΛHCDM OHCDM QHCDM w C = 0, w S = 1, 1/3 (integral) ΛOCDM Perturbative All Adiabatic Models (ν) Anisotropic Entropic Sonic ζ ~ S Π ζ >> S S=S Ε S=S S ζ > S Π ζ < S c 2 Π S Ε >> S Π C > 0 ζ = const. ζ = const. ζ = S Ε -integral ζ = Φ = iterative Φ = stress Φ = ζ,s Ε -integral soln. integral Φ = Π decaying mode Defects iddm Constant Entropy Two Component w 1,w 2 PIB Axion iddm General WKB ks>>1 Two Component w 1,w 2, k >>k y Adiabatic Acoustic Peaks One Component QCDM,GDM (w<0) Sonic/Entropic σ = const w 1,w 2, k >>k y PIB σ generation Heat Conduction All Models Smooth Formation QCDM, GDM CDMv stress integral homog. ODE General ζ = Φ = Sonic/Anisotropic Viscous Damping All Models Collisionless Damping All Models (ν) Mixed S Π,S Ε,S S stress integral Green's integral Sonic/Entropic/ Anisotropic Isocurvature Scaling Seeds Traditional Defect Models Isocurvature Seeds General Defect Models

83 P(k) T/T k CMB Polarization l LSS +High-z CMB Anisotropy Measurements P(k)? Clustering Properties of Matter k CMB Pol T/T Gravity Waves Vorticity? CMB Polarization l Density Perturbations % Level Classical Cosmological Parameters + Origin of Fluctuations (inflation?) Nature of Dark Matter Bias Cosmological Parameters + Origin and Evolution of Fluctuations (inflation?) Cosmological Model Gravity? LSS + High-z Origin and Evolution of Structure (defects?)

84 Summary Upcoming CMB measurements should establish a secure cosmological framework at high redshifts

85 Summary Upcoming CMB measurements should establish a secure cosmological framework at high redshifts If acoustic structures are found at sub degree scales, we can determine photon baryon ratio Ω b h 2 matter radiation ratio Ω m h 2 angular diameter distance Ω Λ or Ω K even if the adiabatic CDM model is incorrect

86 Summary Upcoming CMB measurements should establish a secure cosmological framework at high redshifts If acoustic structures are found at sub degree scales, we can determine photon baryon ratio Ω b h 2 matter radiation ratio Ω m h 2 angular diameter distance Ω Λ or Ω K even if the adiabatic CDM model is incorrect Combine with LSS (z-surveys, lensing), distance measures... to construct precision tests and/or extract subtle properties of the dark sector trace components equation of state clustering properties neutrino background radiation (neutino mass, trace curvature/λ) (Λ vs. quintessence) (quintessence vs. GDM) (neutrino number and anisotropies)

87 Summary Upcoming CMB measurements should establish a secure cosmological framework at high redshifts If acoustic structures are found at sub degree scales, we can determine photon baryon ratio Ω b h 2 matter radiation ratio Ω m h 2 angular diameter distance Ω Λ or Ω K even if the adiabatic CDM model is incorrect Combine with LSS (z-surveys, lensing), distance measures... to construct precision tests and/or extract subtle properties of the dark sector trace components equation of state clustering properties neutrino background radiation (neutino mass, trace curvature/λ) (Λ vs. quintessence) (quintessence vs. GDM) (neutrino number and anisotropies) If acoustic structures are not found at sub degree scales, we need to to reexamine basic assumptions and use all diagnostics to reconstruct the cosmological model, e.g CMB polarization

88 Part I: CMB/Framework Current CMB Data Thermal History Angular Diameter Distance Integrated Sachs Wolfe Effect Sachs Wolfe Effect Acoustic Oscillations Harmonic Peaks Projection Baryon Drag Driving Effects Diffusion Damping Doppler Effect Physical Decomposition Index Part II: LSS/Precision Baryon Oscillations Baryon Bumps Hubble Constant Cosmological Constant SDSS improvements Weak Lensing / Parameters Part III: Dark Matter/Beyond CDM Inconsistent Measures Beyond CDM GDM Neutrino mass / Acceleration Relativistic GDM Neutrino Background Rad. Beyond GDM Outtakes