Primordial nongaussianities I: cosmic microwave background. Uros Seljak, UC Berkeley Rio de Janeiro, August 2014

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1 Primordial nongaussianities I: cosmic microwave bacground Uros Selja, UC Bereley Rio de Janeiro, August 2014

2 Outline Primordial nongaussianity Introduction and basic physics CMB temperature power spectrum and observables Primordial perturbations CMB Polarization: E and B modes

3 Theory Observations Source: NASA/WMAP Science Team

4 Gaussian random field, ζ(x) normal distribu6on of values in real space, Prob[ζ(x)] Prob 1 2 ( ζ ) exp ζ = 2 2πσ 2σ defined en6rely by power spectrum in Fourier space ζ ( 2 ) ( ) ( ') π P ζ = δ + ' ζ bispectrum and (connected) higher- order correla6ons vanish ζ ζ ζ = ' '' 0 4

5 non- Gaussian random field, ζ(x) anything else David Wands 5

6 Rocy Kolb non-rocy Kolb 6

Primordial Gaussianity from infla2on Quantum fluctua2ons from infla2on ground state of simple harmonic oscillator almost free field in almost de Si5er space almost scale- invariant and almost

7 Primordial Gaussianity from infla2on Quantum fluctua2ons from infla2on ground state of simple harmonic oscillator almost free field in almost de Si5er space almost scale- invariant and almost Gaussian Power spectra probe bacground dynamics (H, ε,...) ζ 1 ζ 2 = ( ) ( ) ( ) ( ) n 4 2π P δ +, P ζ but, many different models, can produce similar power spectra Higher- order correla?ons can dis?nguish different models ζ non- Gaussianity non- linearity interac?ons = physics+gravity 1 ( ) ( ) 2π B,, ( + ) ζ 1 ζ 2 = ζ 1 2 δ ζ 7 Wiipedia: AllenMcC

8 Many sources of non- Gaussianity Initial vacuum Excited state inflation Sub-Hubble evolution Hubble-exit Super-Hubble evolution Higher-derivative interactions e.g. -inflation, DBI, Galileons Features in potential Self-interactions + gravity End of inflation Tachyonic instability (p)reheating Modulated (p)reheating After inflation Curvaton decay Magnetic fields primordial non-gaussianity Primary anisotropies Last-scattering Secondary anisotropies ISW/lensing + foregrounds 8

Many shapes for primordial bispectra local type (Komatsu&Spergel

equilateral type (Creminelli et al 2005) peas for 1~2~ orthogonal

shapes separable basis (Ferguson et al 2008) 9 ( ) + + 1 2 2 1 2 1

9 Many shapes for primordial bispectra local type (Komatsu&Spergel 2001) local in real space max for squeezed triangles: <<, equilateral type (Creminelli et al 2005) peas for 1~2~ orthogonal type (Senatore et al 2009) independent of local + equilateral shapes separable basis (Ferguson et al 2008) 9 ( ) ,, B ζ ( ) ( )( )( ) ,, B ζ ( ) ( ) ,, B ζ

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

Blac body spectrum observed by COBE Residuals Mather et al 1994 - close to

11 Blac body spectrum observed by COBE Residuals Mather et al close to thermal equilibrium: temperature today of 2.726K ( ~ 000K at z ~ 1000 because ν ~ (1+z))

12 (almost) uniform 2.726K blacbody Dipole (local motion) O(10-5 ) perturbations (+galaxy) Observations: the microwave sy today Source: NASA/WMAP Science Team

13 Can we predict the primordial perturbations? Maybe.. Inflation mae >10 0 times bigger Quantum Mechanics waves in a box calculation vacuum state, etc After inflation Huge size, amplitude ~ 10-5

Perturbation evolution what we actually observe CMB monopole source till 80 000 yrs (last scattering), linear in conformal time scale invariant

14 Perturbation evolution what we actually observe CMB monopole source till yrs (last scattering), linear in conformal time scale invariant primordial adiabatic scalar spectrum photon/baryon plasma + dar matter, neutrinos Characteristic scales: sound wave travel distance; diffusion damping length

15 Observed ΔT as function of angle on the sy

16 Calculation of theoretical perturbation evolution Perturbations O(10-5 ) Simple linearized equations are very accurate (except small scales) Can use real or Fourier space Fourier modes evolve independently: simple to calculate accurately Physics Ingredients Thomson scattering (non-relativistic electron-photon scattering) - tightly coupled before recombination: tight-coupling approximation (baryons follow electrons because of very strong e-m coupling) Bacground recombination physics (Saha/full multi-level calculation) Linearized General Relativity Boltzmann equation (how angular distribution function evolves with scattering)

17 CMB power spectrum C l Theory: Linear physics + Gaussian primordial fluctuations a = dω Theory prediction ΔT * lm Y lm C l = a lm 2 - variance (average over all possible sy realizations) - statistical isotropy implies independent of m Initial conditions + cosmological parameters linearized GR + Boltzmann equations CMBFAST: cmbfast.org CAMB: camb.info CMBEASY: cmbeasy.org COSMICS, etc.. C l

18 Sources of CMB anisotropy Sachs Wolfe: Potential wells at last scattering cause redshifting as photons climb out Photon density perturbations: Over-densities of photons loo hotter Doppler: Velocity of photon/baryons at last scattering gives Doppler shift Integrated Sachs Wolfe: Evolution of potential along photon line of sight: net red- or blue-shift as photon climbs in an out of varying potential wells Others: Photon quadupole/polarization at last scattering, second-order effects, etc.

19 CMB temperature power spectrum Primordial perturbations + later physics acoustic oscillations diffusion damping primordial power spectrum Hu & White, Sci. Am., (2004) finite thicness

20 Why C l oscillations? Thin in -space: modes of different size Co-moving Poisson equation: (/a) 2 Ф = κ δρ / 2 - potentials approx constant on super-horizon scales - radiation domination ρ ~ 1/a 4 à δρ/ρ ~ 2 a 2 Ф à since Ф ~ constant, super-horizon density perturbations grow ~ a 2 After entering horizon pressure important: perturbation growth slows, then bounces bac à series of acoustic oscillations (sound speed ~ c/ ) CMB anisotropy (mostly) from a surface at fixed redshift: phase of oscillation at time of last scattering depends on time since entering the horizon à -dependent oscillation amplitude in the observed CMB

21 Challinor: astro-ph/04044

22 Contributions to temperature C l + other Challinor: astro-ph/04044

23 What can we learn from the CMB? Initial conditions What types of perturbations, power spectra, distribution function (Gaussian?); => learn about inflation or alternatives. (distribution of ΔT; power as function of scale; polarization and correlation) What and how much stuff Matter densities (Ω b, Ω cdm ); ; neutrino mass (details of pea shapes, amount of small scale damping) Geometry and topology global curvature Ω K of universe; topology (angular size of perturbations; repeated patterns in the sy) Evolution Expansion rate as function of time; reionization - Hubble constant H 0 ; dar energy evolution w = pressure/density (angular size of perturbations; l < 50 large scale power; polarizationr) Astrophysics S-Z effect (clusters), foregrounds, etc.

24 Cosmic Variance: only one sy Use estimator for variance: C obs l = 1 2l + 1 m a lm 2 Assume a lm gaussian: C obs l ~ χ 2 with 2l + 1d.o.f. Cosmic Variance ΔC obs l 2 2 2Cl 2l + 1 WMAP low l P( C l C l obs ) - inverse gamma distribution (+ noise, sy cut, etc). Cosmic variance gives fundamental limit on how much we can learn from CMB l

25 How to generate CMB polarization? 25 (Wayne Hu, CMB Tutorials)

26 How to generate CMB polarization? 26 (Wayne Hu, CMB Tutorials

27 How to generate CMB polarization? 27 (Wayne Hu, CMB Tutorials)

28 Polarization: Stoes Parameters - - Q U Q -Q, U -U under 90 degree rotation Q U, U -Q under 45 degree rotation Spin-2 field Q + i U or Ran 2 trace free symmetric tensor θ θ = ½ tan -1 U/Q sqrt(q 2 + U 2 )

29 29 WMAP Polarization

30 E-mode E and B mode patterns Unchanged if seen through the mirror B-mode Pattern reverses if seen through the mirror Selja and Zaldarriaga, 1998

31 E and B harmonics Expand scalar P E and P B in spherical harmonics Expand P ab in tensor spherical harmonics Harmonics are orthogonal over the full sy: E/B decomposition is exact and lossless on the full sy Zaldarriaga, Selja: astro-ph/ Kamionowsi, Kosowsy, Stebbins: astro-ph/

32 CMB Polarization Signals E polarization from scalar, vector and tensor modes B polarization only from vector and tensor modes (curl grad = 0) + non-linear scalars Average over possible realizations (statistically isotropic): Parity symmetric ensemble: Power spectra contain all the useful information if the field is Gaussian

33 Scalar adiabatic mode E polarization only correlation to temperature T-E

34 Primordial Gravitational Waves (tensor modes) Well motivated by some inflationary models - Amplitude measures inflaton potential at horizon crossing - distinguish models of inflation Observation would rule out other models - epyrotic scenario predicts exponentially small amplitude - small also in many models of inflation, esp. two field e.g. curvaton Wealy constrained from CMB temperature anisotropy - cosmic variance limited to 10% - degenerate with other parameters (tilt, reionization, etc) Loo at CMB polarization: B-mode smoing gun Has BICEP2 observed it?

35 CMB polarization from primordial gravitational waves (tensors) Tensor B-mode Tensor E-mode Adiabatic E-mode Wea lensing Planc noise (optimistic) Amplitude of tensors unnown Clear signal from B modes there are none from scalar modes Tensor B is always small compared to adiabatic E Selja, Zaldarriaga: astro-ph/

36 Reionization Ionization since z ~ 6-20 scatters CMB photons Temperature signal similar to tensors Quadrupole at reionization implies large scale polarization signal Measure optical depth with WMAP T-E correlation

37 Other non-linear effects Thermal Sunyaev-Zeldovich Inverse Compton scattering from hot gas: frequency dependent signal Kinetic Sunyaev-Zeldovich (SZ) Doppler from bul motion of clusters; patchy reionization; (almost) frequency independent signal Ostrier-Vishniac (OV) same as SZ but for early linear bul motion Rees-Sciama Integrated Sachs-Wolfe from evolving non-linear potentials: frequency independent Gravitational lensing discussed on friday

38 Newtonian potential a Gaussian random field Φ(x) = φ G (x) Liguori, Matarrese and Moscardini (200)

39 Newtonian potential a local function of Gaussian random field Φ(x) = φ G (x) + f NL ( φ G2 (x) - <φ G2 > ) f NL =+000 ΔT/T -Φ/, so positive f NL more cold spots in CMB Liguori, Matarrese and Moscardini (200)

40 Newtonian potential a local function of Gaussian random field Φ(x) = φ G (x) + f NL ( φ G2 (x) - <φ G2 > ) f NL =-000 ΔT/T -Φ/, so negative f NL more hot spots in CMB Liguori, Matarrese and Moscardini (200)

41 Newtonian potential a local function of Gaussian random field Φ(x) = φ G (x) + f NL ( φ G2 (x) - <φ G2 > ) Large-scale modulation of small-scale power split Gaussian field into long (L) and short (s) wavelengths φ G (X+x) = φ L (X) + φ s (x) two-point function on small scales for given φ L < Φ(x 1 ) Φ(x 2 ) > L = (1+4 f NL φ L ) < φ s (x 1 ) φ s (x 2 ) > +... X 1 X 2 i.e., inhomogeneous modulation of small-scale power P (, X ) -> [ f NL φ L (X) ] P s () but f NL <5 so any effect must be 10-4

42 Optimal estimation from CMB data

43 Planc Paper XXIV constraints: no evidence for primordial nongaussianity

44 Conclusions CMB contains lots of useful information! - primordial perturbations + well understood physics (cosmological parameters) Precision cosmology - constrain many cosmological parameters + primordial perturbations Currently no evidence for any deviations from standard near scale-invariant purely adiabatic primordial spectrum E-polarization and T-E measure optical depth, constrain reionization; constrain isocurvature modes Large scale B-mode polarization from primordial gravitational waves: - energy scale of inflation - rule out most epyrotic and pure curvaton/ inhomogeneous reheating models and others No evidence for primordial nongaussianity from CMB

Cosmic Microwave Background Introduction

Cosmic Microwave Background Introduction Matt Chasse chasse@hawaii.edu Department of Physics University of Hawaii at Manoa Honolulu, HI 96816 Matt Chasse, CMB Intro, May 3, 2005 p. 1/2 Outline CMB, what