The Outtakes. Back to Talk. Foregrounds Doppler Peaks? SNIa Complementarity Polarization Primer Gamma Approximation ISW Effect

Transcription

1 The Outtakes CMB Transfer Function Testing Inflation Weighing Neutrinos Decaying Neutrinos Testing Λ Testing Quintessence Polarization Sensitivity SDSS Complementarity Secondary Anisotropies Doppler Effect Vishniac Effect Patchy Reionization Sunyaev-Zel'dovich Effect Rees-Sciama & Lensing Foregrounds Doppler Peaks? SNIa Complementarity Polarization Primer Gamma Approximation ISW Effect Back to Talk

2 Doppler Effect Relative velocity of fluid and observer Extrema of oscillations are turning points or velocity zero points Velocity π/2 out of phase with temperature Velocity maxima Velocity minima

3 Doppler Effect Relative velocity of fluid and observer Extrema of oscillations are turning points or velocity zero points Velocity π/2 out of phase with temperature No baryons Zero point not shifted by baryon drag Increased baryon inertia decreases effect m eff V 2 1/2 = const. V m eff = (1+R) 1/2 T/T η Ψ /3 V Velocity maxima Baryons V T/T η Velocity minima Ψ /3

4 Doppler Peaks? Doppler effect has lower amplitude and weak features from projection d observer j l (kd)y l 0 Y 0 0 d observer j l (kd)y l 0 Y 1 0 Temperature peak Doppler (2l+1)j l (100) (2l+1)j l '(100) no peak l l Hu & Sugiyama (1995)

5 Relative Contributions Spatial Power 10 5 total temp dopp Hu & Sugiyama (1995); Hu & White (1997) kd

6 Relative Contributions l Angular Power 10 5 Spatial Power 10 5 total temp dopp Hu & Sugiyama (1995); Hu & White (1997) kd

7 Projection into Angular Peaks Peaks in spatial power spectrum Projection on sphere Spherical harmonic decomposition Maximum power at l = kd Extended tail to l << kd Described by spherical bessel function j l (kd) peak d observer j l (kd)y l 0 Y 0 0 (2l+1)j l (100) l Bond & Efstathiou (1987) Hu & Sugiyama (1995); Hu & White (1997)

8 Projection into Angular Peaks Peaks in spatial power spectrum Projection on sphere Spherical harmonic decomposition Maximum power at l = kd Extended tail to l << kd 2D Transfer Function T 2 (k,l) ~ (2l+1) 2 [ T/T] 2 j l 2 (kd) log(k Mpc) Transfer Function Streaming Oscillations SW Acoustic log(x) log(l) Bessel Functions Projection Oscillations Main Projection Hu & Sugiyama (1995)

9 Measuring the Potential Remove smooth damping (independent of perturbations) Measure relative peak heights Relate to RΨ at last scattering Compare with large scale structure Ψ today Residual is smooth potential envelope and measures matter radiation ratio Hu & White (1996)

10 Uses of Acoustic Oscillations Distinct features Presence/absence unmistakenable Sensitive to background parameters through fluid parameters Sensitive to perturbations through gravitational potential wells which later form structure Robust measures of Angular diameter distance (curvature) Baryon photon ratio

11 Uses of Baryon Drag Measures baryon photon ratio at last scattering + z last scattering + T CMB Ω b h 2 Measures potential wells at last scattering (compare with large scale structure today) Removes phase ambiguity by distinguishing compression from rarefaction peaks (separates inflation from causal seed models)

12 Uses of Damping Sensitive to thermal history and baryon content Independent of (robust to changes in) perturbation spectrum Robust physical scale for angular diameter distance test (Ω K, Ω Λ )

13 Integrated Sachs Wolfe Effect Potential redshift: g 00 = (1+Ψ) 2 δ ij blueshift redshift Kofman & Starobinskii (1985) Hu & Sugiyama (1994)

14 Integrated Sachs Wolfe Effect Potential redshift: g 00 = (1+Ψ) 2 δ ij Perturbed cosmological redshift g ij =a 2 (1+Ψ) 2 δ ij δt/t = δa/a = Ψ blueshift redshift Kofman & Starobinskii (1985) Hu & Sugiyama (1994)

15 Integrated Sachs Wolfe Effect Potential redshift: g 00 = (1+Ψ) 2 δ ij Perturbed cosmological redshift g ij =a 2 (1+Ψ) 2 δ ij δt/t = δa/a = Ψ Time varying potential Rapid compared with λ/c δt/t = 2 Ψ Slow compared with λ/c redshift blueshift cancel Imprint characteristic time scale of decay in angular spectrum blueshift redshift Power (2Ψ) 2 l ISW ~ d/ η l Kofman & Starobinskii (1985) Hu & Sugiyama (1994)

16 Testing Inflation / Initial Conditions 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) Adiabatic Τ/Τ Ψ Θ+Ψ η Harmonic series: curvature 1:2:3... isocurvature 1:3:5... (b) Isocurvature Τ/Τ Ψ η Hu & White (1996) Θ+Ψ

17 Testing Inflation / Initial Conditions 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

18 Weighing Neutrinos Massive neutrinos suppress power strongly on small scales [ P/P 8Ω ν /Ω m ]: well modeled by [c eff 2 =w g, c vis 2 =w g, w g : 1/3 1] Degenerate with other effects [tilt n, Ω m h 2...] CMB signal small but breaks degeneracies 2σ Detection: 0.3eV [Map (pol) + SDSS] Power Suppression Complementarity 1 SDSS SDSS only Joint P(k) 0.1 m v = 0 ev m v = 1 ev n MAP only k (h Mpc -1 ) Hu, Eisenstein, & Tegmark (1998); Eisenstein, Hu & Tegmark (1998) Ω ν h 2 = mν/94ev

19 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 Hata (1998) Solar ν e - ν µ,τ sin 2 2θ

20 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 Hata (1998) Hu, Eisenstein & Tegmark (1998) Solar ν e - ν µ,τ sin 2 2θ

21 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 Hata (1998) Hu, Eisenstein & Tegmark (1998) Hu & Tegmark (1998) Solar ν e - ν µ,τ sin 2 2θ

22 1 0.1 T/T Φ Decaying Dark Matter Example: relativistic matter goes nonrelativistic, decays back into radiation Model decay and decay products as a single component of dark matter Novel consequences: scale invariant curvature perturbation from scale invariant isocurvature perturbations T (µk) l m=5kev Hu (1998) ζ a eq w ddm a P(k) τ=3yrs τ=5yrs τ=8yrs k (h Mpc -1 )

23 Testing Λ If w g <0, GDM has no effect on acoustic dynamics (k peaks, heights) independent of w g, Ω g, c eff, c vis Power ( ) w g = 1/6 = 1/3 = 2/3 = 1 c eff 2=1 degeneracy CMB sensitive to GDM/Λ mainly through angular diameter distance [d A =f(wg,ωg...)] l (rescaled to d A ) 0 MAP (no pol with pol) wg 0.5 Hu, Eisenstein, Tegmark & White (1998) Ωg

24 Testing Λ If w g <0, GDM has no effect on acoustic dynamics (k peaks, heights) independent of w g, Ω g, c eff, c vis Power ( ) w g = 1/6 = 1/3 = 2/3 = 1 c eff 2=1 degeneracy CMB sensitive to GDM/Λ mainly through angular diameter distance [d A =f(wg,ωg...)] Galaxy surveys determines h CMB determines Ω m h 2 Ω m Flatness Ωg = 1 Ω m wg MAP + SDSS l (rescaled to d A ) MAP (no pol with pol) SDSS Only Hu, Eisenstein, Tegmark & White (1998) Ωg

25 Testing Λ If w g <0, GDM has no effect on acoustic dynamics (k peaks, heights) independent of w g, Ω g, c eff, c vis Power ( ) w g = 1/6 = 1/3 = 2/3 = 1 c eff 2=1 degeneracy CMB sensitive to GDM/Λ mainly through angular diameter distance [d A =f(wg,ωg...)] Galaxy surveys determines h CMB determines Ω m h 2 Ω m Flatness Ωg = 1 Ω m SNIa determines luminosity distance [d L =f(wg,ωg)] Hu, Eisenstein, Tegmark & White (1998) wg Consistency Complemetarity MAP + SDSS l (rescaled to d A ) MAP (no pol with pol) SDSS Only SNIa Only MAP SNIa Ωg

26 Testing Λ If w g <0, GDM has no effect on acoustic dynamics (k peaks, heights) independent of w g, Ω g, c eff, c vis Power ( ) w g = 1/6 = 1/3 = 2/3 = 1 c eff 2=1 degeneracy CMB sensitive to GDM/Λ mainly through angular diameter distance [d A =f(wg,ωg...)] Galaxy surveys determines h CMB determines Ω m h 2 Ω m Flatness Ωg = 1 Ω m wg l (rescaled to d A ) SN data July 1998 SNIa determines luminosity distance [d L =f(wg,ωg)] 1.0 Garnavich et al (1998); Riess et al (1998); Perlmutter et al (1998) Ωg

27 P(k) Is the Missing Energy a Scalar Field? Scalar Fields have maximal sound speed [c eff =1, speed of light] CMB+LSS Lower limit on c eff >0.6 at w g = 1/6 [2.7σ: MAP+SDSS; 7.7σ: Planck+SDSS] [in 10d parameter space, including bias, tensors] Strong constraints for w g > 1/2 Large Scale Structure k (h Mpc 1) Power ( ) CMB Anisotropies w g = 1/6 w g = 1/6 c eff 2=0 c eff 2=0 1/6 1/6 1 scalar 2 1 fields scalar fields l Hu, Eisenstein, Tegmark & White (1998)

28 Polarization from Thomson Scattering Thomson scattering of anisotropic radiation linear polarization Polarization aligned with cold lobe of the quadrupole anisotropy Quadrupole Anisotropy ε e ε Thomson Scattering ε Linear Polarization

29 Perturbations & Their Quadrupoles Orientation of quadrupole relative to wave (k) determines pattern Scalars (density) m=0 Vectors (vorticity) Tensors (gravity waves) m=±1 m=±2 Scalars: hot m=0 Vectors: m=1 Tensors: m=2 v cold hot v v Hu & White (1997)

30 Polarization Patterns Scalars E, B 0 θ π/2 l=2, m=0 π 0 π/2 π 3π/2 2π Vectors 0 θ π/2 Tensors π l=2, m=1 0 π/2 0 π 3π/2 2π θ π/2 l=2, m=2 π 0 π/2 π 3π/2 2π φ

31 Electric & Magnetic Patterns Global view: behavior under parity Local view: alignment of principle vs. polarization axes Global Parity Flip Local Axes E Kamionkowski, Kosowski, Stebbins (1997) Zaldarriaga & Seljak (1997) Hu & White (1997) Principal B Polarization

32 Patterns and Perturbation Types Amplitude modulated by plane wave Principle axis Direction detemined by perturbation type Polarization axis Scalars π/2 Polarization Pattern B/E=0 Multipole Power Vectors θ B/E=6 Tensors π/2 0 π/4 π/2 φ Kamionkowski, Kosowski, Stebbins (1997); Zaldarriaga & Seljak (1997); Hu & White (1997) B/E=8/ l

33 Polarization Raw Sensitivity T (µk) l

34 SDSS: Improving Parameter Estimation MAP (no pol) h 1.3 Ω m 1.4 Ω Λ 1.1 Ω K 0.31 MAP (pol) Classical Cosmology MAP+SDSS (pol, 0.2hMpc -1 ) Eisenstein, Hu & Tegmark (1998) 100% 75% 50% 25% 0% Relative Errors

35 Supernovae Type Ia July wg % 95% 68% Ωg Garnavich et al. (1998); Riess et al. (1998); Perlmutter et al. (1998) Figure: Hu, Eisenstein, Tegmark, White (1998)

36 Supernovae Type Ia, CMB & LSS Projection SDSS 0 MAP(P) wg 0.5 SN Ωg Hu, Eisenstein, Tegmark, White (1998)

37 SDSS: Improving Parameter Estimation MAP (no pol) h 1.3 Ω m 1.4 Ω Λ 1.1 Ω K 0.31 Ω m h Ω b h Ω ν h n s 0.14 α 0.30 T/S 0.48 log(a) 1.3 τ 0.69 Eisenstein, Hu & Tegmark (1998) MAP (pol) % 75% 50% 25% 0% Relative Errors MAP+SDSS (pol, 0.2hMpc -1 )

38 Secondary Anisotropies Temperature and polarization anisotropies imprinted in the CMB after z=1000 Rescattering Effects Linear Doppler Effect (cancelled) Modulated Doppler Effects (non linear) by linear density perturbations Ostriker Vishniac Effect by ionization fraction Inhomogeneous Reionization by clusters thermal & kinetic Sunyaev Zel'dovich Effects Gravitational Effects Gravitational Redshifts by cessation of linear growth Integrated Sachs Wolfe Effect by non linear growth Rees Sciama Effect Gravitational Lensing

39 Cancellation of the Linear Effect Last Scattering Surface e velocity redshifted γ overdensity blueshifted γ Cancellation Observer

40 Modulated Doppler Effect Last Scattering Surface e velocity overdensity, ionization patch, cluster... unscattered γ blueshifted γ Observer

41 Ostriker Vishniac Effect Primary Doppler Ostriker Vishniac Hu & White (1996)

42 Patchy Reionization Aghanim et al (1996) Gruzinov & Hu (1998) Knox, Scocciomarro & Dodelson (1998)

43 Thermal SZ Effect Persi et al. (1995) Atrio Barandela & Muecket (1998)

44 Rees Sciama Effect Gravitational Lensing Seljak (1996a,b)

45 Residual Foreground Effects MAP Planck total x2 dust synchrotron free-free increased noise point sources Temperature 1 x2 total dust increased noise point sources Temperature 0.01 % degradation total increased noise synchrotron x2 x2 E-polarization B-polarization 1 total dust increased noise synchrotron x2 x2 E-polarization B-polarization 10 1 total increased noise synchrotron total dust increased noise synchrotron l l

46 Foregrounds & Parameter Estimation Tegmark, Eisenstein, Hu, de Oliviera Costa (1999)

47 Features in the Transfer Function Features in the linear transfer function Break at sound horizon Oscillations at small scales; washed out by nonlinearities 1.0 BBKS86 T(k) / T BBKS86 (k) S95 T(k) EH98 PD Ω m =0.3, h=0.5, Ω b /Ω 0 = k (h Mpc -1 ) 0.1 Eisenstein & Hu (1998)