Dark Sector Combining Low and High Redshift Information Collaborators Past & Present

Probing the Dark Side

1 SDSS

) Ð3 k 10 100 MAP ( Planck P 80 10 Ð4 0.1

60 ψ T Ð5 P ∆ LSS 10 40 0.01 k (h Mpc-1) 10 Ð6 20 CMB Lensing 10 Ð7 10 100l (multipole) 10 100 l (multipole) of Structure Formation Wayne Hu 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 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 subÐdegree scale CMB anisotropies ¥ Achieving precision with large-scale structure from galaxy surveys, lensing... ¥ Constructing consistency tests between these measures, distance measures... The Dark Side of Structure Formation

¥ Observationally testing the properties of the dark sector combining low and high redshift information Collaborators Past & Present

¥ Microwave Background ¥ Large-Scale Structure Emory Bunn Daniel Eisenstein Douglas Scott Alex Szalay Uros Seljak Max Tegmark Joe Silk Naoshi Sugiyama Martin White Matias Zaldarriaga Collaborators Past & Present

¥ Microwave Background ¥ Large-Scale Structure Emory Bunn Daniel Eisenstein Douglas Scott Alex Szalay Uros Seljak Max Tegmark Joe Silk Naoshi Sugiyama ¥ Presentation Martin White Matias Zaldarriaga Microsoft

http://www.sns.ias.edu/~whu/dark.pdf Part I: Establishing the Cosmological Framework

Begin with the CMB because... ¥ Linearity observed: ∆T/T ~ 10Ð5 ¥ Simple Physics Gravity Fluid Dynamics Geometry ¥ Rich Features Acoustic Peaks CMB Anisotropies

Tegmark, de Oliviera Costa, Devlin, Netterfield, & Page (1996) Current CMB Quilt

10 1 θ (degrees)

100

80 K)

µ 60 (

T ∆ 40

W. Hu Ð May 1999 10 100 l (multipole) COBE PythV-95 TOCOSask MSAM CAT QMAP MAX Tene SP94Argo MSAM RING ATCA FIRS BAM SP91Pyth IAB MSAM WD OVRO SuZIE Projected MAP Errors

10 1 θ (degrees)

100

80 K)

µ 60 (

T ∆ 40

W. Hu Ð Feb. 1998 10 100 l (multipole) Projected Planck Errors

10 1 θ (degrees)

100

80 K)

µ 60 (

T ∆ 40

W. Hu Ð Feb. 1998 10 100 l (multipole) Thermal History

¥ z > 1000; Tγ > 3000K Hydrogen ionized Free electrons glue photons to baryons γ eÐ p compton scattering coulomb interactions PhotonÐbaryon fluid Potential wells that later form structure

ly coupled fl tight uid cold

mean free path << wavelength hot hot Thermal History

¥ z > 1000; Tγ > 3000K ¥ z ~ 1000; Tγ ~ 3000K Hydrogen ionized Recombination Free electrons glue photons to baryons Fluid breakdown γ Ð e p z < 1000; Tγ < 3000K compton scattering coulomb interactions ¥ Gravitational redshifts & PhotonÐbaryon fluid lensing Potential wells that later form structure Reionization; rescattering

scattering surf last ace λ∼k-1

z=1000θ∼l-1 recombination

observer Angular Diameter Distance

¥ Spatial Curvature ¥ Robust Physical Scales Standardized ruler Sound horizon Peak spacing Measure angular extent Diffusion scale Damping tail Ruler & comoving distance scale (except for Λ) Infer curvature

Flat

1 Power

Closed 0.1

10 100 1000 Kamionkowski, Spergel & Sugiyama (1994) Hu & White (1996) l Curvature and the Cosmological Constant

Ω 0 K Shifted Acoustic Signature

0.5

0.9 0

ΩΛ Power W. Hu 2/98 500 1000 10 0.5 1500 1 l 2000

Gravitational Redshift 0.9 Power

500 1000 1500 l 2000 The Acoustic Peaks

¥ Initial Conditions and the SachsÐWolfe Effect ¥ Acoustic Oscillations ¥ Peak Positions ¥ Baryon Drag ¥ Radiation Driving ¥ Diffusion Damping

Initial Conditions & the Sachs-Wolfe Effect ¥ Initial temperature perturbation

¥ Observed temperature perturbation o ewt nia Gravitational redshift: Ψ N n

+ Initial temperature: + Θ Time Comoving

¥ Potential = time-time Ψ = δt/t metric perturbations Space Initial Conditions & the Sachs-Wolfe Effect

Initial temperature perturbation ¥ cold

¥ Observed temperature perturbation o ewt nia Gravitational redshift: Ψ N n

+ Initial temperature: + Θ Time Comoving

Ψ = δ ¥ Potential = time-time t/t hot metric perturbations Space ¥ MatterÐdominated expansion: a ∝ t2/3, δa/a = 2/3 δt/t ¥ Temperature falls as: T ∝ aÐ1 ¥ Temperature fluctuation: δT/T = Ðδa/a Initial Conditions & the Sachs-Wolfe Effect

Initial temperature perturbation ¥ cold

¥ Observed temperature perturbation o ewt nia Gravitational redshift: Ψ N n

+ Initial temperature: + Θ Time Comoving

Observed temperature perturbation: (δT/T )obs= Θ+Ψ = 1/3 Ψ Sachs & Wolfe (1967) White & Hu (1997) Acoustic Oscillations

¥ Photon pressure resists compression in potential wells ¥ Acoustic oscillations

Effective Mass

Photon Pressure

Potential Well Ψ Peebles & Yu (1970) Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997) Acoustic Oscillations

¥ Photon pressure resists ¥ Oscillation amplitude = initial compression in potential wells displacement from zero pt. ¥ Acoustic oscillations Θ Ð (-Ψ) = 1/3Ψ ¥ Gravity displaces zero point Θ ≡ δT/T = ÐΨ

initial displ. Θ+Ψ T /

T zero ∆ point η

−|Ψ|/3

Peebles & Yu (1970) Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997) Acoustic Oscillations

Θ+Ψ T /

T First Extrema ∆

−|Ψ|/3

Peebles & Yu (1970) Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997) Acoustic Oscillations

Θ+Ψ T /

T Second Extrema ∆

−|Ψ|/3

Peebles & Yu (1970) Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997) Harmonic Peaks

¥ Oscillations frozen at last scattering ¥ Wavenumbers at extrema = peaks

¥ Sound speed cs Last Scattering Θ+Ψ First T /

T Peak ∆

η π/ sound k1= horizon −|Ψ|/3

Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997) Harmonic Peaks

ω η ¥ Oscillations frozen ¥ Frequency = kcs ; conformal time at last scattering last scattering ∝ φ η ω sound ¥ Phase k ; = ∫ d = k horizon ¥ Wavenumbers at 0 extrema = peaks ¥ Harmonic series in sound horizon φ = nπ → k = nπ/ sound ¥ Sound speed cs n n horizon Last Last Scattering Scattering Θ+Ψ First Θ+Ψ T T / /

T Peak T ∆ ∆

η η π/ sound k1= horizon k2=2k1 −|Ψ|/3 −|Ψ|/3 Second Peak

Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997) Baryon Drag ¥ Baryons provide inertia ¥ Relative momentum density ρ ρ ∝ Ω 2 R = ( b + pb)Vb / ( γ + pγ)Vγ bh ¥ Effective mass meff = (1 + R) T / T ∆ η

zero pt −|Ψ|/3 Low Baryon Content Hu & Sugiyama (1995) Baryon Drag ¥ Baryons provide inertia ¥ Baryons drag photons into → ↑ ¥ Relative momentum density potential wells zero point ρ ρ ∝ Ω 2 ↑ R = ( b + pb)Vb / ( γ + pγ)Vγ bh ¥ Amplitude Ð1/2 ¥ Effective mass meff = (1 + R) ¥ Frequency ↓ (ω ∝ meff ) .. 2 2 ¥ Constant R, Ψ: (1+ R) Θ + (k /3)Θ = Ð(1+ R) (k /3)Ψ Θ + Ψ = [Θ(0) + (1+ R) Ψ(0)] cos [ kη/√3 (1+ R)] Ð RΨ

Θ+Ψ T / T ∆ η

zero pt −|Ψ|/3 High Baryon Content Hu & Sugiyama (1995) Baryon Drag ¥ Baryons provide inertia ¥ Baryons drag photons into → ↑ ¥ Relative momentum density potential wells zero point ρ ρ ∝ Ω 2 ↑ R = ( b + pb)Vb / ( γ + pγ)Vγ bh ¥ Amplitude Ð1/2 ¥ Effective mass meff = (1 + R) ¥ Frequency ↓ (ω ∝ meff ) .. 2 2 ¥ Constant R, Ψ: (1+ R) Θ + (k /3)Θ = Ð(1+ R) (k /3)Ψ Θ + Ψ = [Θ(0) + (1+ R) Ψ(0)] cos [ kη/√3 (1+ R)] Ð RΨ

Θ+Ψ |

T / T ∆

| η

zero pt −|Ψ|/3 Alternating Peak Heights Hu & Sugiyama (1995) Baryons in the CMB

20 Baryon Drag 15 High odd peaks Power/Damping ¥ 10 Power Power 5

500 1000 l 0.001 Ω 2 bh 0.01 ¥ Additional Effects TimeÐvarying potential Dissipation/Fluid 0.1 imperfections 10 1

Power 0.1 W. Hu 2/98 500 1000 1500 2000 l Driving Effects and Matter/Radiation ¥ Potential perturbation: k2Ψ = Ð4πGa2δρ generated by radiation ¥ Radiation → Potential: inside sound horizon δρ/ρ pressure supported δρ hence Ψ decays with expansion

−Ψ T / T ∆

η Θ+Ψ

Hu & Sugiyama (1995) Driving Effects and Matter/Radiation ¥ Potential perturbation: k2Ψ = Ð4πGa2δρ generated by radiation ¥ Radiation → Potential: inside sound horizon δρ/ρ pressure supported δρ hence Ψ decays with expansion ¥ Potential → Radiation: ΨÐdecay timed to drive oscillation Ð2Ψ + (1/3)Ψ = Ð(5/3)Ψ → 5x boost ¥ Feedback stops at matter domination −Ψ T / T ∆

η Θ+Ψ

Hu & Sugiyama (1995) Matter Density in the CMB

¥ Amplitude ramp across 20 matterÐradiation equality 2 Ωmh 15 ¥ Radiation density fixed by Power/Damping CMB temperature & thermal 10 Power history Power 5

0.1 500 1000 Ω 2 mh

Ω 2 ¥ Measure mh from peak 1

heights Power W. Hu 2/98 500 10 1000 1 1500 l 2000 0.1 Dissipation / Diffusion Damping → λ ¥ Imperfections in the coupled fluid mean free path C in the baryons ¥ Random walk over diffusion scale: geometric mean of mfp & horizon λ λ √ √λ η >> λ D ~ C N ~ C C λ λ ; λ λ ¥ Overtake wavelength: D ~ second order in C/ ¥ Viscous damping for R<1; heat conduction damping for R>1

η λ 1.0 N= / C

λ λ √ Power D ~ C N perfect fluid 0.1 instant decoupling λ

500 1000 1500 l Silk (1968); Hu & Sugiyama (1995); Hu & White (1996) Dissipation / Diffusion Damping ¥ Rapid increase at recombination as mfp ↑

¥ Independent of (robust to changes in) perturbation spectrum

Ω Ω ¥ Robust physical scale for angular diameter distance test ( K, Λ)

Recombination 1.0 Power perfect fluid 0.1 instant decoupling recombination

500 1000 1500 l Silk (1968); Hu & Sugiyama (1995); Hu & White (1996) Physical Decomposition & Information

combined 4

3 temperature

Power 2 doppler 1

500 1000 1500 l Physical Decomposition & Information ¥ Fluid + Gravity → alternating peaks → photon-baryon ratio → Ω h2 b 4 baryon drag 3

Power 2

500 1000 1500 l Physical Decomposition & Information ¥ Fluid + Gravity → alternating peaks → photon-baryon ratio → Ω h2 b 4 → driven oscillations → matterÐradiation ality equ ratio ion 3 at → Ω 2 di mh ra r te at Power 2 m

500 1000 1500 l Physical Decomposition & Information ¥ Fluid + Gravity → alternating peaks → photon-baryon ratio → Ω h2 perfect fluid b 4 → driven oscillations → matterÐradiation ratio 3 2 πkA → Ωmh

¥ Fluid Rulers Power 2 → sound horizon k → damping scale D 1 di ffusion dam ping

500 1000 1500 l Physical Decomposition & Information ¥ Fluid + Gravity → alternating peaks → photon-baryon ratio → Ω h2 b 4 → driven oscillations → matterÐradiation lA=dA× ratio 3 2 πkA → Ωmh ISW ¥ Fluid Rulers Power 2 lD=dA× → sound horizon k → damping scale D ¥ Geometry 1 → angular diameter distance f(ΩΛ,ΩK) + flatness or no ΩΛ, 500 1000 1500 → ΩΛ or ΩK l Cosmological Parameters in the CMB BaryonÐPhoton Ratio MatterÐRadiation Ratio

0.001 Ω h2 0.1 b Ω 2 0.01 mh

0.1 1 l l

C C 10

+1)

1 ( +1)

( 10 l 0.1 500 500 1000 1500 2000 1000 1 1500 l l 2000 0.1 Curvature Cosmological Constant

0 0 Ω ΩΛ K

0.5 Ω 0.5 Λ

0.9

0.9 l

+1)

+1) ( l

l ( l 500 10 500 10 1000 1000 1500 1 1500 1 l 2000 W.Hu 2/98 l 2000 CMB Anisotropy T/T T/T ? ∆ Measurements ∆ l l LSS ? CMB +High-z P(k) Polarization k P(k) k CMB Pol Gravity Waves Density CMB Clustering Vorticity Perturbations Polarization Properties of Matter

¥ Acoustic oscillations in the matter power spectrum ¥ Isolating classical cosmological parameters ¥ Weak lensing by large scale structure ¥ Measuring the growth rate of perturbations Acoustic Peaks in the Matter ¥ Baryon density & velocity oscillates with CMB

¥ Baryons decouple at τ / R ~ 1, the end of Compton drag epoch δ ∼ ¥ Decoupling: b(drag) Vb(drag), but not frozen

End of Drag Epoch

Hu & Sugiyama (1996) 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 (drag) ∼ V (drag), but not frozen ¥ . b b δ ¥ Continuity: b =ÐkVb Velocity Overshoot Dominates: δ ∼ V (drag) kη >> δ (drag) ¥ b b b ¥ Oscillations π/2 out of phase with CMB ¥ Infall into potential wells (DC component)

End of Drag Epoch Velocity Overshoot + Infall

Hu & Sugiyama (1996) Features in the Power Spectrum ¥ Features in the linear power spectrum ¥ Break at sound horizon ¥ Oscillations at small scales; washed out by nonlinearities

nonlinear scale (arbitrary norm.) ) k (

P 0.1 Eisenstein & Hu (1998) numerical

0.01 0.1 k (h Mpc-1) 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)

nonlinear scale (arbitrary norm.) ) k (

P 0.1 mv = 0 eV mv = 1 eV

W. Hu Ð Feb. 1998 0.01 0.1 k (h Mpc-1) 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

nonlinear scale (arbitrary norm.) ) k (

P 0.1 mv = 0 eV mv = 1 eV

W. Hu Ð Feb. 1998 0.01 0.1 k (h Mpc-1) Combining Features in LSS + CMB ¥ Consistency check on thermal history and photonÐbaryon ratio → Ð1 ¥ Infer physical scale lpeak(CMB) kpeak(LSS) in Mpc

ΛCDM 8

(arbitrary norm.) 4 k3Pγ(k) Power 2

0.05 0.1 Ð1 Eisenstein, Hu & Tegmark (1998) k (Mpc ) Hu, Eisenstein, Tegmark & White (1998) Combining Features in LSS + CMB ¥ Consistency check on thermal history and photonÐbaryon ratio → Ð1 ¥ Infer physical scale lpeak(CMB) kpeak(LSS) in Mpc Ð1 → ¥ Measure in redshift survey kpeak(LSS) in h Mpc h

ΛCDM 8

(arbitrary norm.) 4 k3Pγ(k) h Power 2

Pm(k) 0.05 0.1 Ð1 Eisenstein, Hu & Tegmark (1998) k (Mpc ) Hu, Eisenstein, Tegmark & White (1998) Combining Features in LSS + CMB ¥ Consistency check on thermal history and photonÐbaryon ratio → Ð1 ¥ Infer physical scale lpeak(CMB) kpeak(LSS) in Mpc Ð1 → ¥ Measure in redshift survey kpeak(LSS) in h Mpc h ¥ Robust to low redshift physics (e.g. quintessence, GDM)

ΛCDM 8 QCDM wg=Ð1/2

(arbitrary norm.) 4 k3Pγ(k) h Power 2

Pm(k) 0.05 0.1 Ð1 Eisenstein, Hu & Tegmark (1998) k (Mpc ) Hu, Eisenstein, Tegmark & White (1998) MAP +P +SDSS H0 ±130 ±23 ±1.2 Classical Cosmology Ωm ±1.4 ±0.25 ±0.016 SDSS 100 MAP(P) CMB:

~line of constant 0 80 1.0 Ω H 2 H m 0 0.8 Ωm+ΩΛ Ω Λ 0.6 60 0.4

0.2

0 40

0 0.2 0.4 0.6 0.8 Eisenstein, Hu, Tegmark (1998) Ωm MAP +P +SDSS H0 ±130 ±23 ±1.2 Classical Cosmology Ωm ±1.4 ±0.25 ±0.016 ΩΛ ±1.1 ±0.20 ±0.024 100

Any other precision 0 80 1.0 (including H ) H 0 0.8 breaks degeneracy Ω Λ 0.6 60 0.4

0.2

0 40

0 0.2 0.4 0.6 0.8 Eisenstein, Hu, Tegmark (1998) Ωm MAP +P +SDSS H0 ±130 ±23 ±1.2 Classical Cosmology Ωm ±1.4 ±0.25 ±0.016 ΩΛ ±1.1 ±0.20 ±0.024 1.0

MAP +SNIa Many opportunities 0.8 for consistency checks! MAP (e.g. high-z SNIa) +SDSS Consistency 0.6 Complementarity Λ

Ω SNIa 0.4 MAP

0.2 SDSS

0 0.2 0.4 0.6 0.8 1.0 Ωm Eisenstein, Hu, Tegmark (1998) Weak Lensing: Prospects for Measuring Cosmological Parameters

¥ Potentially as precise as the CMB ¥ Main systematic effects are instrumental rather than astrophysical

Colley, Turner, & Tyson (1996) Cluster (Strong) Lensing: 0024+1654 Weak Lensing: Prospects for Measuring Cosmological Parameters

¥ Potentially as precise as the CMB ¥ Main systematic effects are instrumental rather than astrophysical

White & Hu (1999) 5 degree field Weak Lensing: Prospects for Measuring Cosmological Parameters

¥ Potentially as precise as the CMB ¥ Main systematic effects are instrumental rather than astrophysical ¥ The Bad News Depends on most (8) 10Ð3 cosmological parameters Projected 3û Lensing Survey

10Ð4 π /2 ψ 10Ð5 P +1) l ( l 10Ð6 MAP degenerate (0.1σ)

10Ð7 10 100 1000 l Hu & Tegmark (1998) Weak Lensing: Prospects for Measuring Cosmological Parameters

¥ Potentially as precise as the CMB ¥ Main systematic effects are instrumental rather than astrophysical ¥ The Bad News Depends on most (8) 11D CDM Space cosmological parameters WL√fsky MAP(T) Planck(T+P) ¥ The Good News 2 σ(Ωmh ) 0.024 0.029 0.0027 Depends on most (8) 2 σ(Ωbh ) 0.0092 0.0029 0.0002 cosmological parameters σ(mν) 0.29 0.77 0.25 σ(ΩΛ) 0.079 1.0 0.11 σ(Ω ) 0.096 0.29 0.030 P(k) K ¥ σ(ns) 0.066 0.1 0.009 ¥ Growth σ(lnA) 0.28 1.21 0.045 σ(zs) 0.047 (1) (1) ¥ Distribution of faint galaxies σ(τ) Ð 0.63 0.004 σ(T/S) Ð 0.45 0.012 σ(Y ) (0.02) (0.02) 0.01 Hu & Tegmark (1998) p Weak Lensing: Prospects for Measuring Cosmological Parameters

¥ Potentially as precise as the CMB ¥ Main systematic effects are instrumental rather than astrophysical ¥ The Bad News fsky: 10Ð5 10Ð4 10Ð3 0.01 0.1 1 Depends on most (8) (a) Weak Lensing + MAP cosmological parameters ΩΛ ) zs ΩΚ ¥ The Good News 10

Depends on most (8) CMB+WL σ / cosmological parameters mν CMB σ

( 1 ¥ P(k) (b) Weak Lensing + Planck zs ¥ Growth 10 ΩΛ Ω Distribution of faint galaxies Κ ¥ mν improvement

1 Hu & Tegmark (1998) 1 10 100 Θdeg CMB Anisotropy T/T T/T ? ∆ Measurements ∆ l l LSS ? CMB +High-z P(k) Polarization k P(k) k CMB Pol Gravity Waves Density CMB Clustering Vorticity Perturbations Polarization Properties of Matter

¥ Inconsistent precision measures? ¥ Generalized dark matter ¥ Examples: massive neutrinos, scalar fields, decaying dark matter, neutrino background radiation 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 (11Ð15 parameters) 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 (11Ð15 parameters) What If ¥ CMB shows subÐdegree 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 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 Generalized Dark Matter

¥ Arbitrary StressÐEnergy Tensor Tµν 16 Components ¥ Local Lorentz Invariance → Symmetric Tµν 10 Components

Hu (1998) Generalized Dark Matter

¥ Arbitrary StressÐEnergy Tensor Tµν 16 Components ¥ Local Lorentz Invariance → Symmetric Tµν 10 Components ¥ EnergyÐMomentum Conservation 4 Constraints 1 Pressure 5 Anisotropic stresses

Hu (1998) Generalized Dark Matter

¥ Arbitrary StressÐEnergy Tensor Tµν 16 Components ¥ Local Lorentz Invariance → Symmetric Tµν 10 Components ¥ EnergyÐMomentum 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 1 Background pressure Instability 1 Pressure fluctuation 1 Scalar anisotropic stress fluctuation

Hu (1998) Generalized Dark Matter

equation of state sound speed viscosity 2 2 wg ceff cvis Prototypes: ¥ Cold dark matter 0 0 0 (WIMPs) ¥ Hot dark matter 1/3→0 (light neutrinos) ¥ Cosmological constant Ð1 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 1/3 (neutrino anisotropies) Determining the Accelerating Component

¥ Is a cosmological constant responsible for the acceleration?

σ(wg)=0.13 (MAP+SDSS) σ (wg)=0.13 (MAP+SN Ia) SDSS σ(wg)=0.03 (Planck+SDSS) σ MAP (wg)=0.03 (Planck+SN Ia) 0 (P)

If not (Ð1

¥ g g

field responsible? w sound speed constrained Ð0.5 SNIa if wg > Ð1/2 MAP + SDSS

Ð1.0 Consistency MAP 0.2 0.4 0.6 0.8 1.0 Complemetarity + SNIa Ωg Hu, Eisenstein, Tegmark & White (1998) Detecting the 10 MAP Neutrino Background Radiation no pol 5 pol ¥ Neutrino number Nν or temperature Tν alters the matterÐradiation ratio ν

N 0 Ω 2 ¥ Degenerate with matter density mh Ð5 SDSS ¥ Break degeneracy with NBR anisotropies Ignoring Anisotropies 2 Ωmh ρ ρ m/ r fixed MAP+SDSS

Hu, Eisenstein, Tegmark & White (1998) Anisotropies in the 10 MAP Neutrino Background Radiation no pol 5 pol ¥ Neutrino quadrupole anisotropies alter Ψ and drive acoustic oscillations ν

N 0 ¥ Anisotropies well modeled by GDM viscosity 2 cvis =1/3 but largely degenerate Ð5 SDSS ¥ Detectability: 1σ, MAP (pol); 3.5σ, Ignoring Anisotropies MAP+SDSS; 7.2σ, Planck (pol); 10 8.7σ, Planck+SDSS 5 SDSS 8 ν

N 0 ρ ρ m/ r fixed 4 Neutrinos MAP+SDSS GDM c 2 = 1/3 Power vis GDM c 2 = 0 Ð5 2 vis Employing Anisotropies

10 100 0 0.2 0.4 0.6 Hu (1998) l 2 Hu, Eisenstein, Tegmark & White (1998) Ωmh Stressing the Dark Sector ¥ A structure formation model is completely defined by its stress history 8 6 ¥ Stress properties of the ordinary/luminous 4 Power matter are known 2 ¥ Model is defined by the stress history of 10 100 1000 the dark sector 104

Two models with exactly the same stress )

¥ k ΛCDM history are phenomenologically identical P( GDM single component (ΛCDM vs. GDM with no CDM 103 2 2 0.001 0.01 0.1 with right wg and ceff =0, cvis =0) k (h Mpc-1)

Hu & Eisenstein (1998) Stressing the Dark Sector ¥ A structure formation model is completely defined by its stress history 8 6 ¥ Stress properties of the ordinary/luminous 4 Power matter are known 2 ¥ Model is defined by the stress history of 10 100 1000 the dark sector 104

Two models with exactly the same stress )

¥ k ΛCDM history are phenomenologically identical P( GDM single component (ΛCDM vs. GDM with no CDM 103 2 2 0.001 0.01 0.1 with right wg and ceff =0, cvis =0) k (h Mpc-1)

¥ GDM ansatz: stress history is defined by simple equations of state for stresses in the background and (separately) in the perturbations ¥ Reasonable if model phenomenology is similar to adiabatic CDM

¥ If not, must go beyond the GDM ansatz... Hu & Eisenstein (1998) Einstein Equations Gµν=8πGTµν

FRW Background Vector Perturbations + Tensor Perturbations Linear Perturbations

Stress Free Anisotropic Stress Stress Free Anisotropic Stress (±1) (±1) (±1) (±1) (±2) (±2) (±2) (±2) ρ Π ρ Π H >> (p/ρ )Π H < (p/ρ )Π H >> (p/ cr) H <~(p/ cr) T cr T ~ cr Scalar Perturbations Pure Decay Stress Integral Free Gravity Stress Integral Decay from Defects Waves tCDM (radiation) arbitrary initial Defects tCDM (matter) conditions Scalar Stress ζ <~ S, SΠ Stress Free ζ >> S , S Π Anisotropic Entropic Sonic Mixed ζ < S ~ Π S=SΕ S=SS SΠ ,SΕ ,SS ζ >> S Clustered Smooth ζ = const. ζ = backgrd.

Φ= backgrd. ODE ζ ζ 2 > S Π < SΠ SΕ >> S Π cC > 0 General integral Φ= backgrd. ζ = ζ ζ = ζ ζ = stress ODE const. = const. SΕ-integral = stress Φ Φ Φ ζ integral = iterative = stress = ,SΕ-integral integral Φ Φ= Green's soln. integral = homog. ODE integral 2 Component 2,3 Component w1,w2 wC = w1 wS = w1,w2 All Adiabatic ΛCDM GDM Perturbative ΠÐdecaying Constant Entropy General Sonic/Entropic Sonic/Aniso- Sonic/Entropic/ Models except OCDM φQCDM All Adiabatic mode WKB ks>>1 tropic Anisotropic σ OCDM HCDM ΛHCDM Models (ν) Defects Two Component = const Isocurvature strCDM OHCDM iDDM w1,w2 Two Component w1,w2, k >>ky Viscous φ Scaling Seeds CDM QHCDM PIB w1,w2, k >>ky PIB Damping QCDM Axion Adiabatic Acoustic All Models Traditional w = 0, w = Ð1,Ð1/3 σ− C S iDDM Peaks generation Defect Models (integral) Heat Conduction Isocurvature Seeds ΛOCDM Collisionless One Component All Models General Damping QCDM,GDM Smooth Formation Defect Models All Models (ν) (w<0) QCDM, GDM

CDMv Hu & Eisenstein (1998) CMB Anisotropy T/T T/T ? ∆ Measurements ∆ l l LSS ? CMB +High-z P(k) Polarization k P(k) k CMB Pol Gravity Waves Density CMB Clustering Vorticity Perturbations Polarization Properties of Matter

Nature of LSS % Level Bias Gravity? Dark Matter + Classical High-z Cosmological Parameters Cosmological Parameters + + Origin of Fluctuations Origin and Evolution Origin (inflation?) of Fluctuations and (inflation?) Evolution of Structure (defects?) Cosmological Model Summary ¥ Upcoming CMB measurements should establish a secure cosmological framework at high redshifts Summary ¥ Upcoming CMB measurements should establish a secure cosmological framework at high redshifts ¥ If acoustic structures are found at subÐdegree scales, we can determine Ω 2 photonÐbaryon ratio bh Ω 2 matterÐradiation ratio mh Ω Ω angular diameter distance Λ or K even if the adiabatic CDM model is incorrect Summary ¥ Upcoming CMB measurements should establish a secure cosmological framework at high redshifts ¥ If acoustic structures are found at subÐdegree scales, we can determine Ω 2 photonÐbaryon ratio bh Ω 2 matterÐradiation ratio mh Ω Ω angular diameter distance Λ or 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 (neutino mass, trace curvature/Λ) equation of state (Λ vs. quintessence) clustering properties (quintessence vs. GDM) neutrino background radiation (neutrino number and anisotropies) ¥ If acoustic structures are not found at subÐdegree scales, we need to to reexamine basic assumptions and use all diagnostics to reconstruct the cosmological model, e.g CMB polarization Index Part I: CMB/Framework Part II: LSS/Precision ¥ Current CMB Data ¥ Baryon Oscillations ¥ Thermal History ¥ Baryon Bumps ¥ Angular Diameter Distance ¥ Hubble Constant ¥ Integrated SachsÐWolfe Effect ¥ Cosmological Constant ¥ SachsÐWolfe Effect ¥ SDSS improvements ¥ Acoustic Oscillations ¥ Weak Lensing ¥ Harmonic Peaks Part III: Dark Matter/BeyondÐCDM ¥ Projection ¥ Inconsistent Measures ¥ Baryon Drag ¥ Beyond CDM ¥ Driving Effects ¥ GDM ¥ Diffusion Damping ¥ Neutrino mass / Acceleration ¥ Doppler Effect ¥ NBR Anisotropies ¥ Physical Decomposition ¥ Stressing Observables ¥ Beyond GDM Outtakes