CMB beyond a single power spectrum: Non-Gaussianity and frequency dependence. Antony Lewis

Transcription

1 CMB beyond a single power spectrum: Non-Gaussianity and frequency dependence Antony Lewis

2 Evolution of the universe Opaque Transparent Hu & White, Sci. Am., (2004)

3 CMB temperature End of inflation Last scattering surface gravity+ pressure+ diffusion

4 z=0 θ Mpc z~1000

5 Observed CMB blackbody power spectrum Observations Constrain theory of early universe + evolution parameters and geometry

6 Beyond Gaussianity general possibilities Flat sky approximation: Θ x = 1 2π d2 l Θ(l)eix l (Θ = T) Gaussian + statistical isotropy Θ l 1 Θ l 2 = δ l 1 + l 2 C l - power spectrum encodes all the information - modes with different wavenumber are independent Higher-point correlations Gaussian: can be written in terms of C l Non-Gaussian: non-zero connected n-point functions

7 l 3 Bispectrum l 1 l 1 + l 2 + l 3 = 0 l 2 Flat sky approximation: Θ l 1 Θ l 2 Θ(l 3 ) = 1 2π δ l 1 + l 2 + l 3 b l1 l 2 l 3 If you know Θ l 1, Θ l 2, sign of b l1 l 2 l 3 tells you which sign of Θ l 3 is more likely Trispectrum l 4 l 1 l 2 L l 3 N-spectra

8 k 3 Equilateral k 1 + k 2 + k 3 = 0, k 1 = k 2 = k 3 k 1 k 2 + b>0 + T(k 3 ) = T(k 1 ) T(k 2 ) + b<0 T(k 3 ) AL: The Real Shape of Non-Gaussianities, arxiv:

9 Millennium simulation

10 Near-equilateral to flattened: b>0 b<0 k 1 k 3 k 2

11 k 1 + k 2 + k 3 = 0, k 1 k 2, k 3 Local (squeezed) k 2 k 3 k 1 k 2 k 3 + b>0 + T(k 3 ) = T(k 1 ) T(k 2 ) + b<0 T(k 3 ) Squeezed bispectrum is a correlation of small-scale power with large-scale modes

12 Primordial local non-gaussianity e.g. ζ = ζ f NLζ 0,l T T g ( f NLζ,l ) Liguori et al 2007 Single-field slow-roll inflation: f NL 0 Any significant detection would rule out large classes of inflation models New information that is not present in the power spectrum

13 Diagonal squeezed trispectra k 1 ~ k 2, k 3 ~ k 4, k 1 + k 2 = k 3 + k 4 k 2, k 3 k 1 k 2 Trispectrum = power spectrum of modulation k 4 k 3 k 1 k 2 k 1 k 2 k 4 k 3 k 4 k 3 Squeezed trispectrum measures the spatial modulation of small-scale power

14 But even with f NL = 0, we observe CMB at last scattering modulated by other perturbations z=0 θ Mpc z~1000

15 e.g. CMB Lensing: modulation due to large-scale gravitational lenses Last scattering surface Inhomogeneous universe - photons deflected Observer

16 How to measure squeezed non-gaussianity? Modulation reconstruction e.g. can reconstruct and hence measure the lensing field Fractional magnification convergence κ = α/2 Magnified Unlensed Demagnified

17 Lensing reconstruction -concept C l C l C l C l C l C l C l C l C l C l C l C l C l C l C l C l

18 Lensing reconstruction - Maths and algorithm sketch For a given (fixed) lensing field, T P T X : X here is lensing potential, deflection angle, or κ Flat sky approximation: modes correlated for k 2 k 3 use off-diagonal correlation First-order series expansion in the lensing field: function easy to calculate for X(K) = 0 A L, l 1, l 2 Can reconstruct the modulation field X Full sky analysis similar, summing modes with optimal weights gives Quadratic estimator: Zaldarriaga, Hu, Hanson, and others.

19 Planck lensing potential reconstruction: estimate of modulation field ψ Planck collaboration 2013 Note about half signal, half reconstruction noise, not all structures are real map is effectively Wiener filtered Correlation of ψ with T Bispectrum; ψ power spectrum Trispectrum

20 Power spectrum of reconstruction C l ψψ Planck collaboration 2013 Measured at high significance: probes perturbations along the line of sight to recombination

21 Extra information in lensing can help break parameter degeneracies Colour: Planck TT constraint Crosses: Planck lensing

22 Trispectrum: power of the modulation C l ψψ Bispectrum: modulation temperature C l Tψ

23 Planck: first detection of lensing bispectrum! Large cosmic variance and reconstruction noise, but detected at 2.5σ Planck collaboration 2013

24 Primordial bispectrum? Planck collaboration 2013 Planck only sees expected lensing-induced modulations - no evidence for primordial bispectrum

25 Other squeezed-shape effects v 0 boosting from local v c Different lensing, Ricci focussing and redshifting along the line of sight geodesics Underdensity Overdensity (ζ larger) Single field inflation: physics locally identical - statistically equivalent

26 - Redshifting as photons travel through perturbed universe and then Doppler shifted by earth s motion T 1 + ΔT T T ΔT small 1 + ΔT large ΔT small Only Doppler term non-negligible - Transverse directions also affected: perturbations at last scattering are distorted Shear + Convergence + Ricci focussing + Aberration Perturbed angular diameter distance: Radial displacement (small, δχ χ ) Ricci focussing: δn expansion of ray bundle Convergence (lensing) Local aberration

27 Kinematic dipole (Doppler aberration dipole lensing convergence) Power modulation Illustrated for v c = 0.85 Aberration n n + ( n v) - just like a dipole lensing convergence Challinor & van Leeuwen 2002 Planck collaboration 2013

28 Planck collaboration 2013

29 The future: Non-blackbody signals in the CMB? e.g. 1. Spectral distortions in monopole (COBE small) 2. Frequency-dependent anisotropies 1. Spectral distortions. E.g. μ-distortion Full thermal equilibrium: μ γ = 0 Kinetic equilibrium: μ γ 0 if energy deposited but photon number cannot change Measurement of μ can measure energy injection well before recombination e.g. - Dark matter and relic decay/annihilation - Integral of small-scale primordial power spectrum (via. silk damping energy release)

30 2. Frequency-dependent anisotropies Rayleigh scattering blue sky thinking for future CMB observations arxiv: ; previous work: Takahara et al. 91, Yu, et al. astro-ph/

31 Classical dipole scattering Oscillating dipole p = p 0 sin(ωt) z radiated power ω 4 p 0 2 sin 2 θ dω Thomson Scattering m e z = ee z sin ωt p = e2 E z m e ω2 sin ωt z Rayleigh Scattering m e z = ee z sin ωt m e ω 0 z e 2 E z p = m e (ω 2 ω 2 sin ωt z 0 ) (m nucleus m e ) p + e e Frequency independent Given by fundamental constants: Frequency dependent Depends on natural frequency ω 0 of target σ T = 8π 3 e 2 4πε 0 m e c 2 2 σ R ω4 ω 0 4 σ T (ω ω 0 )

32 Photon scattering rate Total cross section ν eff 8 9 c R A GHz, R He 0.1 (Lee 2005: Non-relativistic quantum calculation, for energies well below Lyman-alpha) Rayleigh only negligible compared to Thomson for n H 1+z ν obs GHz 4 ne

33 Visibility

34 Small-scale CMB Primary signal Primary + Rayleigh signal

35 Small-scale CMB cont. Hot spots are red, cold spots are blue Polarization is scattered and is red too Rayleigh difference signal: (photons scattered in to line of sight) (scattered out) τ R ΔT very correlated to primary ΔT

36 Rayleigh temperature power spectrum Primary+Rayleigh 2 = Primary Primary Rayleigh + Rayleigh 2 Solid: Rayleigh Primary Dot-dashed: Rayleigh Rayleigh Dots: naïve Planck sensitivity to the cross per Δl/l = 10 bin (possibly 5σ with Planck full mission) Small-scale signal is highly correlated to primary Can hope to isolate using Low frequency High frequency Note: not limited by cosmic variance of primary anisotropy multi-tracer probe of same underlying perturbation realization Test of expansion and ionization history at recombination

37 Large-scale CMB temperature Rayleigh signal only generated by sub-horizon scattering (no Rayleigh monopole background to distort by anisotropic photon redshifting) Temperature perturbation at recombination (Newtonian Gauge) Sachs-Wolfe Doppler ISW Rayleigh scattering probes Doppler terms independently of SW/ISW

38 Measure new primordial modes with Rayleigh Rayleigh spectrum? In principle could double number of modes compared to T+E! BUT: signal highly correlated to primary on small scales; need the uncorrelated part Solid: Rayleigh Rayleigh total; Dashed: uncorrelated part; Dots: error per Δl = 10 bin a from PRISM l

39 Number of new modes with future CMB: e.g. PRISM Define New modes almost all in the l 500 temperature signal: total extra modes More horizon-scale information (disentangle Doppler and Sachs-Wolfe terms) Would need much higher sensitivity to get more modes from polarization/high l

40 Rayleigh polarization power spectra Solid: primary Dashed: primary + Rayleigh (857GHz) Large-scale polarization from scattering into the line of sight polarized CMB sky is blue but same quadrupole, so highly correlated to primary

41 On horizon scales three nearly-independent perturbation modes being probed ΔT T + Φ + ISW (anisotropic redshifting to constant temperature recombination surface) n v b : Doppler Polarization from quadrupole scattering Primary Rayleigh, Primary Rayleigh, Primary

42 Expected signal as function of frequency Zero order: uniform blackbody not affected by Rayleigh scattering (elastic scattering, photons conserved) 1 st order: anisotropies modified, no longer frequency independent Need sensitivity at 200GHz ν 800GHz (+probably higher for foreground separation efficiency; very hard above 350GHz from ground)

43 Fractional total C l differences at realistic frequencies TT, EE, BB: ΔC l C l TE: TE ΔC l C l EE C l TT

44 Rayleigh summary Significant Rayleigh signal at ν 200 GHz; several percent on T, E at ν 500GHz Non-blackbody signal in the anisotropies (but no spectral distortion in monopole) Strongly correlated to primary signal on small scales (mostly damping) robust detection via cross-correlation? Powerful test of recombination physics/expansion Boosts large-scale polarization (except B modes from lensing) Multi-tracer probe of last-scattering - limited by noise/foregrounds, not cosmic variance May be able to provide additional primordial information (10,000+ modes) - mostly horizon-scale T modes at recombination from Doppler signal

45 Conclusions Planck TT marks the beginning of the end for C l TT - cosmic variance limited to L 1600 Planck lensing marks end of the beginning for C l φφ - first nearly fully-sky maps of the lensing potential, limited by reconstruction noise - detected bispectrum; trispectrum measured at high significance - must be modelled (+Doppler) to measure primordial non-gaussianity - can break parameter degeneracies (but not yet competitive with e.g. BAO) Future: SPT TT (~months), Planck full mission (1 yr), ACTpol, SPTpol Non-blackbody future: PRISM, Pixie,?? - Spectral distortions: probe inflation at scales k 1Mpc 1 - Rayleigh scattering: test expansion, measure more large-scale modes (+ 21cm - see talk from 2009!)

46 Advertising supplement Looking for SIX funded PhD students this year! AL David Seery Chris Byrnes Peter Coles Robert Smith Ilian Iliev Peter Thomas Kathy Romer Seb Oliver Jon Loveday Mark Sargent Stephen Wilkins Early universe and theory of observations Large scale structure and simulations Observation and modelling of galaxies and clusters