1. 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:

2. 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 of anisotropies.
The observables:
Temperature perturbations Θ
Polarizations (E-modes and B-modes)
2016/10/25
Atsuhisa Ota (Tokyo Tech)

3. 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)

4. 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)

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

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

7. 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)

8. 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)

9. 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 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)

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

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

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

13. 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)

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

15. 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)

16. 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)

17. 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)

18. 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)

19. 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)

20. Atsuhisa Ota (Tokyo Tech)
When is the signal modified?
AO, arXiv:
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)

21. Atsuhisa Ota (Tokyo Tech)
When is the signal modified?
AO, arXiv:
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)

22. 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)

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

24. 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)