Cosmological constraints from μE cross correlations 2016. Oct. 25th JGRG26 Cosmological constraints from μE cross correlations Atsuhisa Ota Tokyo Institute of Technology Based on arXiv:1607.00212

Atsuhisa Ota (Tokyo Tech) The cosmic microwave background is The remnant radiation at recombination. The snap shot of the early universe (z~1100) Isotropic Black body at high precision (2.725K=2.348 ×10-4eV). But the there exist 10-5 of anisotropies. The observables: Temperature perturbations Θ Polarizations (E-modes and B-modes) 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) Parameter 68 % confidence limits for the base ΛCDM model from Planck CMB power spectra ns=0.9657±0.0040, 68% C.L. AR109=2.142±0.049, 68% C.L. 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) The problems Observable scales are limited: Angular resolution Maximum multipole, ℓ~ 3000 (Planck) Silk damping Small scale perturbations are erased, ℓ>O(100) Our observable scales are just 7 e-holdings of the 60 which is necessary for hot Big Bang. What happens at smaller scales? 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) Theory of `energy spectrum’ distortions 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) Ideal Blackbody ? 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Energy injection to the photon plasma There exist non-thermal energy injections to the CMB photons: Darkmatter pair-annihilations PBHs evaporations Silk damping (Photon diffusion) etc… Photon distribution function is always deformed. What happens next? 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Distribution function & spectral distortion History of photon plasma z>2×106(480eV): Pair annihilations: e++e-→2γ Bremsstrahlung: e-→e-+γ Double Compton: e-+γ→e-+2γ Photon number is free Chemical equilibrium 2×106>z>5×104(1.2eV): Compton: e-+γ→e-+γ Photon number is fixed Bose-Einstein dist. μ≠0 is possible. Kinetic equilibrium Z<5×104: Compton is not frequent. No more equilibrium state. Compton y-distortion: Partly kinetic equilibrium 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) The cosmic microwave background is The remnant radiation at the last scattering. The snap shot of the early universe (z~1100) Isotropic Black body at high precision. (2.725K=2.348 ×10-4eV). But the there exist 10-5 of anisotropies. The observables: Temperature perturbations Θ Polarizations (E-modes and B-modes) Spectral distortions (μ&y type) 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) What can we see from μ-X cross correlation? 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) Basics of μ distortion 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Mixing of the local photon equilibrium states Simplify 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) Pick up a partition! Two Blackbodies Single Blackbody Diffusion & Thermalization Spatially inhomogeneous Spatially homogeneous 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) Energy density 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) Number density Both the number and the energy conservation laws No more Planck dist. but Bose dist. with . 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) λD Corse-grained at each a diffusion patch. μ is inhomogeneous over the scale. 2016/10/25 Atsuhisa Ota (Tokyo Tech)

The μ hierarchy equation Heierarchy expansion (Legendre expansion in k・n) The monopole component is conserved. Higher multipoles are suppressed. 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) μ free streaming Integrate along the line of sight. Multipole components at present come from the monopole at LSS Project this onto the sky→ Harmonic coefficient 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) μT cross-correlation and Primordial non-Gaussianity(Pajer and Zaldarriaga 2013) ❶ μΘ comes from R 3-point functions. ❷ Two of the three R are at the same place. ❸ Significant for “local type” non-Gaussianity. PIXIE will constrain up to fNLloc~2000 from μT. Independent constraints from temperature 3-point fnc. 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) When is the signal modified? AO, arXiv:1607.00212 Scale dependent non-Gaussianity Cross correlations with the polarizations Tensor non-Gaussianity Is thermodynamic approach explicit? AO, arXiv:1610.***** Spectral distortions are second order effects The framework of second order Boltzmann equations 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Atsuhisa Ota (Tokyo Tech) When is the signal modified? AO, arXiv:1607.00212 Scale dependent non-Gaussianity Cross correlations with the polarizations Tensor non-Gaussianity Is thermodynamic approach explicit? AO, arXiv:1610.***** Spectral distortions are second order effects The framework of second order Boltzmann equations 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Correlations with Polarizations Polarization E-mode is included only for low l (large scale). S/N is 44% of the temperature alone. No improvement from Joint analysis: A consistency relation 2016/10/25 Atsuhisa Ota (Tokyo Tech)

The Consistency relation μ spherical coefficient Θ spherical coefficient with Sachs-Wolfe approx. 2016/10/25 Atsuhisa Ota (Tokyo Tech)

Summary of the cross-correlation analysis ❶ Cosmological constraints from the μE & μT cross correlations are investigated. ❷ Cross correlation with E-mode polarization has roughly half SN compared to the temperature alone. ❸ Joint analysis does not improve for low l. 2016/10/25 Atsuhisa Ota (Tokyo Tech)