CMB Episode II: Theory or Reality? Wayne Hu

Transcription

1 s p ac 10 1 CMB Episode II: θ (degrees) n n er p ac u ter 10 1 θ (degrees) e T (µk) 60 T (µk) l (multipole) l (multipole) Theory or Reality? Wayne Hu

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

3 Current CMB Quilt 10 1 θ (degrees) T (µk) W. Hu May l (multipole) COBE PythV-95 TOCO Sask MSAM CAT QMAP MAX Tene SP94 Argo MSAM RING ATCA FIRS BAM SP91 Pyth IAB MSAM WD OVRO SuZIE

4 Projected Boomerang Errors 10 1 θ (degrees) T (µk) W. Hu May l (multipole)

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

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

7 CMB Today? Very early reionization Simplest isocurvature models Griffiths et al. (1999); Hu, Bunn & Sugiyama (1995); Pen, Seljak & Turok (1997)

8 CMB Today? Very early reionization Simplest isocurvature models "Missing Energy" in curvature Ω K ~ < 0.5 (95%CL) if Ω Λ =0 Baryon Content 0.015< Ω b h 2 < (68%CL) Constraints on (Ω m,ω Λ ) when combined ~ with SNIa, age... Ω Λ > 0.5 (95%CL) Lineweaver (1998); Bond & Jaffe (1998); White (1998); Efstathiou et al (1999); Tegmark (1999)

9 CMB Today? Very early reionization Simplest isocurvature models "Missing Energy" in curvature Ω K ~ < 0.5 (95%CL) if Ω Λ =0 CMB Forecast? Percent Level Constraints on Ω b h 2, Ω m h 2, d A (mainly Ω K ) Inflationary/adiabatic initial conditions Baryon Content 0.015< Ω b h 2 < (68%CL) Constraints on (Ω m,ω Λ ) when combined ~ with SNIa, age... Ω Λ > 0.5 (95%CL) Lineweaver (1998); Bond & Jaffe (1998); White (1998); Efstathiou et al (1999); Tegmark (1999) Jungman et al. (1996); Hu & White (1996)

10 CMB Today? Very early reionization Simplest isocurvature models "Missing Energy" in curvature Ω K ~ < 0.5 (95%CL) if Ω Λ =0 Baryon Content 0.015< Ω b h 2 < (68%CL) Constraints on (Ω m,ω Λ ) when combined ~ with SNIa, age... Ω Λ > 0.5 (95%CL) CMB Forecast? Percent Level Constraints on Ω b h 2, Ω m h 2, d A (mainly Ω K ) Inflationary/adiabatic initial conditions Tensors / Inflationary dynamics T/S < 0.4 (MAP); (Planck) Dark Matter/Energy: mv < 0.2 ev (Planck + 10º Lensing) 1+w Q < 0.07 (Planck + SDSS) Lineweaver (1998); Bond & Jaffe (1998); White (1998); Efstathiou et al (1999); Tegmark (1999) Zaldarriaga et al. (1997); Eisenstein et al. (1999) Hu & Tegmark (1999); Hu et al. (1999)

11 CMB Today? Very early reionization Simplest isocurvature models "Missing Energy" in curvature Ω K ~ < 0.5 (95%CL) if Ω Λ =0 Baryon Content 0.015< Ω b h 2 < (68%CL) Constraints on (Ω m,ω Λ ) when combined ~ with SNIa, age... Ω Λ > 0.5 (95%CL) CMB Forecast? Percent Level Constraints on Ω b h 2, Ω m h 2, d A (mainly Ω K ) Inflationary/adiabatic initial conditions Tensors / Inflationary dynamics T/S < 0.4 (MAP); (Planck) Dark Matter/Energy: mv < 0.2 ev (Planck + 10º Lensing) 1+w Q < 0.07 (Planck + SDSS) Caveat: Microwave Foregrounds Lineweaver (1998); Bond & Jaffe (1998); White (1998); Efstathiou et al (1999); Tegmark (1999) Tegmark & Efstathiou (1996); Dodelson (1996); Knox (1999); Bouchet & Gispert (1999); Tegmark et al. (1999)

12 Forecasts & Results: Are They Believable? Yes! Statements based on acoustic peaks once they are confirmed by the observation of at least 2 of them Maybe... Statements based on combining anisotropies with polarization and other cosmological data sets: systematic effects!

13 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

14 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

15 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

16 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

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

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)

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)

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)

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 Doroshkevich, Zel'dovich & Sunyaev (1978); Bond & Efstathiou (1984); Hu & Sugiyama (1995)

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 Doroshkevich, Zel'dovich & Sunyaev (1978); Bond & Efstathiou (1984); Hu & Sugiyama (1995)

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 Inflation as Source of Perturbations Superluminal expansion (inflation) required to generate superhorizon curvature (density) perturbations Else perturbations are isocurvature initially with matter moving causally Curvature (potential) perturbations drive acoustic oscillations Ratio of peak locations (a) Inflation Τ/Τ Ψ Θ+Ψ η Harmonic series: curvature 1:2:3... isocurvature 1:3:5... (b) Causal Motion Τ/Τ Ψ η Hu & White (1996) Θ+Ψ

32 Inflation as Source of Perturbations Superluminal expansion (inflation) required to generate superhorizon curvature (density) perturbations Else perturbations are isocurvature initially with matter moving causally Curvature (potential) perturbations drive acoustic oscillations Ratio of peak locations Harmonic series: curvature 1:2:3... isocurvature 1:3:5... Power Hidden 1st peak CDM Inflation Axion Isocurvature Hu & White (1996) l

33 Inflation as Source of Perturbations Superluminal expansion (inflation) required to generate superhorizon curvature (density) perturbations Else perturbations are isocurvature initially with matter moving causally Curvature (potential) perturbations drive acoustic oscillations Ratio of peak locations Harmonic series: curvature 1:2:3... isocurvature 1:3:5... Random Forcing: washed out peaks Power Hu & White (1996); Albrecht et al. (1996) Hidden 1st peak CDM Inflation Axion Isocurvature l

34 Dissipation / Diffusion Damping Imperfections in the coupled fluid mean free path λ C in the baryons Random walk over diffusion scale: λ D ~ λ C N ~ λ C η >> λ C 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) l

35 Dissipation / Diffusion Damping Imperfections in the coupled fluid mean free path λ C in the baryons Random walk over diffusion scale: λ D ~ λ C N ~ λ C η >> λ C Rapid increase at recombination as mfp 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 & White (1996) l

36 Physical Decomposition & Information Fluid + Gravity harmonic series: inflationary origin 4 combined Power temperature doppler 500 l

37 Physical Decomposition & Information Fluid + Gravity harmonic series: inflationary origin alternating peaks: photon/baryon Ω b h 2 Power baryon drag l

38 Physical Decomposition & Information Fluid + Gravity harmonic series: inflationary origin alternating peaks: photon/baryon Ω b h 2 4 perfect fluid driven oscillations: matter/radiation Ω m h 2 Ruler Calibration sound horizon damping scale Power 3 2 πk A k D 1 diffusion damping 500 l

39 Physical Decomposition & Information Fluid + Gravity harmonic series: inflationary origin alternating peaks: photon/baryon Ω b h 2 4 driven oscillations: matter/radiation Ω m h 2 Ruler Calibration 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

40 Neoclassical Cosmology & 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

41 Beyond the Acoustic Peaks

42 Polarization Diagnostics CMB polarization generated by scattering of quadrupole anisotropies Quadrupole Anisotropy e ε Linear Polarization Thomson Scattering

43 Polarization Diagnostics CMB polarization generated by scattering of quadrupole anisotropies Isolates the last scattering surface measures the reionization epoch / optical depth (first structures) Reionization Current Constraints < 20 40µK Saskatoon TOCO T (µk) l MAP Planck Hogan, Kaiser, & Rees (1982) Efstathiou & Bond (1987)

44 Polarization Diagnostics CMB polarization generated by scattering of quadrupole anisotropies Isolates the last scattering surface tests causal generation (inflation vs. defects) 6 Current Constraints < 20 40µK Saskatoon TOCO T (µk) 4 2 Causality Constraints 10 l MAP Planck Hu & White (1997) Zaldarriaga & Spergel (1997)

45 Polarization Diagnostics CMB polarization generated by scattering of quadrupole anisotropies Robust ratios of the two parity patterns: scalar (0), vector (6), tensor (0.6) 0 scalar θ π/2 l=2, m=0 π Quadrupoles vector θ 0 π/2 π l=2, m=1 0 tensor θ π/2 l=2, m=2 π 0 π/2 φ 3π/2 2π Zaldarriaga & Seljak (1997) Kamionkowski, Kosowsky & Stebbins (1997) Hu & White (1997)

46 Tensors & Inflation Tensor Amplitude V (inflaton potential) Current upper limits: inflationary energy scale < 2 x GeV Tensor / Scalar amplitude (V'/V) 2 Tensor slope (V'/V) 2 Consistency Relation test of slow-roll inflation Meaningful test by Planck only possible if T/S close to current limits Next next-generation satellite dedicated to polarization?

47

48 Foregrounds and Tensors degradation factor MAP σ(t/s)=0.16 foreground parameters unknown degradation factor Planck σ(t/s)= known 0 0 None Opt. Mid. Pes. None Opt. Mid. Pes Foreground Parameters Simultaneously Estimated Foreground power spectra, frequency dependence, frequency coherence free-free, synchrotron, vibrating dust, rotating dust, thermal SZ, radio point sources, IR point sources 10 Cosmological Parameters Potentially significant degradation: better prior knowledge; more frequencies Tegmark, Eisenstein, Hu, de Oliviera-Costa (1999) Bouchet & Gispert (1999); Knox (1999)

49 Foregrounds and Baryons degradation factor MAP σ(ω b h 2 )= foreground parameters unknown degradation factor Planck σ(ω b h 2 )= known 0 0 None Opt. Mid. Pes. None Opt. Mid. Pes Foreground Parameters Simultaneously Estimated Foreground power spectra, frequency dependence, frequency coherence free-free, synchrotron, vibrating dust, rotating dust, thermal SZ, radio point sources, IR point sources 10 Cosmological Parameters Degradation of less than 2 in errors Tegmark, Eisenstein, Hu, de Oliviera-Costa (1999)

50 ν e ν µ limit Cosmologically Excluded LSND ν µ - ν e ν µ ν τ limit 10-1 ν µ ν s Cosmology and the Neutrino Anomalies m 2 (ev 2 ) Solar ν e - ν µ,τ,s BBN Limit Solar ν e ν µ, τ ν e ν s Atmos ν µ ν τ Anomalies: Hata (1998) Croft, Hu & Davé (1999) Solar ν e - ν µ,τ sin 2 2θ

51 ν e ν µ limit Cosmologically Excluded LSND ν µ - ν e Detectable in Redshift Surveys ν µ ν τ limit ν µ ν s Cosmology and the Neutrino Anomalies m 2 (ev 2 ) Solar ν e - ν µ,τ,s BBN Limit Solar ν e ν µ, τ ν e ν s Atmos ν µ ν τ Anomalies: Hata (1998) Croft, Hu & Davé (1999) Hu, Eisenstein & Tegmark (1998) Solar ν e - ν µ,τ sin 2 2θ

52 ν e ν µ limit Cosmologically Excluded LSND ν µ - ν e Detectable in Redshift Surveys ν µ ν τ limit ν µ ν s Cosmology and the Neutrino Anomalies m 2 (ev 2 ) Detectable in Weak Lensing Solar ν e - ν µ,τ,s BBN Limit Solar ν e ν µ, τ ν e ν s Atmos ν µ ν τ Anomalies: Hata (1998) Croft, Hu & Davé (1999) Hu, Eisenstein & Tegmark (1998) Hu & Tegmark / Hu (1999) Solar ν e - ν µ,τ sin 2 2θ

53 Conclusions: Cautious Optimism Simple adiabatic CDM models have survived the onslaught of data to date Three parameters: Ω b h 2, Ω m h 2, combination of Ω K, Ω Λ already interestingly constrained Precision parameter estimation on these satellites are robust to all but pathological foregrounds Y2.7K Precision constraints on gravity waves and dark energy/matter possible Requires CMB polarization and complementary information from other cosmological measures May require more detailed modelling of foregrounds and/or a next-generation CMB satellite mission

54 Index Current CMB Data Future Missions Today vs. 5yr Forecast Thermal History Curvature Acoustic Oscillations Harmonic Peaks Baryon Drag Matter Content Inflation as Generator Dissipation Physical Components Neoclassical Cosmology Polarization Sensitivity SVT Patterns Tensors & Inflation The Phantom Menace Foregrounds & Baryons Foregrounds & Tensors Dark Matter / Energy Conclusions Complete Talk: Outtakes