CMB Anisotropies: The Acoustic Peaks. Boom98 CBI Maxima-1 DASI. l (multipole) Astro 280, Spring 2002 Wayne Hu

Transcription

1 CMB Anisotropies: The Acoustic Peaks 80 T (µk) Boom98 CBI Maxima-1 DASI l (multipole) Astro 280, Spring 2002 Wayne Hu

2 Physical Landscape 100 IAB Sask 80 Viper BAM TOCO Sound Waves DT (mk) Initial FIRS Conditions COBE QMAP SP Ten ARGO IAC BOOM Pyth MAX MSAM RING Baryon CAT Loading BOOM WD Maxima Radiation OVRO Driving ATCA SuZIE Dissipation BIMA W. Hu 11/ l

3 Gravitational Ringing Potential wells = inflationary seeds of structure Fluid falls into wells, pressure resists: acoustic oscillations

4 Inflation and the Initial Conditions Inflation: (nearly) scale-invariant curvature (potential) perturbations Superluminal expansion superhorizon scales "initial conditions" Accompanying temperture perturbations due to cosmological redshift cold Time Newtonian Comoving hot Space Potential perturbation Ψ = time-time metric perturbation δt/t = Ψ δt/t = δa/a = 2/3δt/t = 2/3Ψ Sachs & Wolfe (1967); White & Hu (1997)

5 Plane Waves Potential wells: part of a fluctuation spectrum Plane wave decomposition

6 Harmonic Modes Frequency proportional to wavenumber: ω=kc s Twice the wavenumber = twice the frequency of oscillation

7 Seeing Sound Oscillations frozen at recombination Compression=hot spots, Rarefaction=cold spots

8 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)

9 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)

10 Extrema=Peaks First peak = mode that just compresses Recombination T/T Ψ /3 Θ+Ψ k 1 =π/ sound horizon First Peak time N.B.: "compression" short for compression inside potential wells and rarefaction inside potential hills

11 Extrema=Peaks First peak = mode that just compresses Second peak = mode that compresses then rarefies: twice the wavenumber Recombination Recombination T/T Θ+Ψ First Peak T/T Θ+Ψ time time Ψ /3 k 1 =π/ sound horizon Ψ /3 k 2 =2k 1 Second Peak

12 Extrema=Peaks First peak = mode that just compresses Second peak = mode that compresses then rarefies: twice the wavenumber Harmonic peaks: 1:2:3 in wavenumber Recombination Recombination T/T Θ+Ψ First Peak T/T Θ+Ψ time time Ψ /3 k 1 =π/ sound horizon Ψ /3 k 2 =2k 1 Second Peak

13 Angular Peaks

14 Peaks in Angular Power The Anisotropy Formation Process

15 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)

16 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)

17 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

18 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

19 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)

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

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

22 Acoustic Landscape DT (mk) FIRS COBE Ten Viper BAM QMAP SP BOOM IAB Sask 1 st extrema TOCO compression ARGO IAC MAX MSAM Pyth compression RING CAT BOOM 3 rd extrema 2WD nd extrema rarefaction Maxima OVRO ATCA SuZIE BIMA W. Hu 11/ l

23 The First Peak

24 First Peak Precisely Measured 80 l 1 ~200 DT (mk) Boom98 CBI Maxima-1 DASI l (multipole)

25 Spatial Curvature Physical scale of peak = distance sound travels Angular scale measured: comoving angular diameter distance test for curvature Flat Closed

26 Curvature in the Power Spectrum Features scale with angular diameter distance Angular location of the first peak

27 A (Nearly?) Flat Universe h<0.8 Ω b h 2 <0.025 ΩΛ BOOMERanG MAXIMA closed open Ω m Hubble constant! (Ω m h 2 : higher peaks) How Flat? Age of the universe

28 What Makes It Flat? h<0.8 Ω b h 2 <0.025 ΩΛ BOOMERanG Clusters MAXIMA closed open Ω m Info on H 0, Ω m, or Ω Λ breaks degeneracy H 0 : currently by assuming flatness, future by measuring Ω m h 2 Cosmic Complementarity

29 A (Nearly?!) Flat Universe ΩΛ h<0.8 Ω b h 2 <0.025 MAXIMA Perlmutter et al. (1998) Riess et al. (1998) BOOMERanG closed open SNe Clusters Ω m Currently showing consistency with Ω Λ >0

30 Dirty Laundry: Standard Rulers Calibrating the Standard Rulers Sound Horizon Damping Scale Baryons Matter/Radiation Baryons Matter/Radiation

31 The Second Peak

32 Baryon & Inertia Baryons add inertia to the fluid Equivalent to adding mass on a spring Same initial conditions Same null in fluctuations Unequal amplitudes of extrema

33 A Baryon-meter Low baryons: symmetric compressions and rarefactions T time Low Baryons

34 A Baryon-meter Load the fluid adding to gravitational force Enhance compressional peaks (odd) over rarefaction peaks (even) T time Baryon Loading

35 A Baryon-meter Enhance compressional peaks (odd) over rarefaction peaks (even) e.g. relative suppression of second peak T time

36 Baryon Loading 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) 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)

37 Baryons in the Power Spectrum

38 Second Peak Detected 80 DT (mk) l 2 ~ Boom98 CBI Maxima-1 DASI l (multipole)

39 Score Card 100 IAB Sask 80 Viper BAM TOCO 1st flatness DT (mk) FIRS COBE RING CAT QMAP SP MAX MSAM Ten ARGO IAC BOOM Pyth 2nd BOOM dark WD baryons Maxima OVRO ATCA SuZIE BIMA W. Hu 11/ l

40 Higher Peaks

41 Radiation and Dark Matter Radiation domination: potential wells created by CMB itself Pressure support potential decay driving Heights measures when dark matter dominates

42 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)

43 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)

44 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)

45 Dark Matter in the Power Spectrum

46 Third Peak Constrained 80 DT (mk) l 3 20 Boom98 CBI Maxima-1 DASI l (multipole)

47 Damping Tail

48 Diffusion Damping Random walk during recombination Dissipation as hot meets cold Physical scale for standard ruler or calibration

49 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

50 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

51 Damping Tail Detected 80 DT (mk) l 3 20 Boom98 CBI Maxima-1 DASI l (multipole)

52 The Peaks 100 IAB Sask 80 Viper BAM TOCO 1st flat universe DT (mk) FIRS COBE Ten QMAP SP BOOM ARGO IAC MAX MSAM Pyth RING dark matter CAT BOOM 3rd WD 2nd baryonic dark matter Maxima checks OVRO ATCA SuZIE BIMA W. Hu 11/ l

53 Summary Precision cosmology has arrived Sound physics seen (pun intended) Consistent with inflationary initial conditions

54 Summary Precision cosmology has arrived Sound physics seen (pun intended) Consistent with inflationary initial conditions First peak nailed: nearly flat universe Second detected: baryonic dark matter (consistent with Big Bang Nucleosynthesis) Third constrained: cold dark matter required