CMB bispectrum Rikkyo University Takashi Hiramatsu Collaboration with Ryo Saito (Yukawa Institute for Theoretical Physics, Kyoto) Atsushi Naruko (Tokyo Institute of Technology) Misao Sasaki (Yukawa Institute for Theoretical Physics, Kyoto) Seminar, 07 Dec 2016 @ ICG
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CMB bispectrum
Rikkyo University
Takashi Hiramatsu
Collaboration with Ryo Saito (Yukawa Institute for Theoretical Physics, Kyoto) Atsushi Naruko (Tokyo Institute of Technology) Misao Sasaki (Yukawa Institute for Theoretical Physics, Kyoto)
Seminar, 07 Dec 2016 @ ICG
CMB bipectrum 2/28
Many kinds of information on inflation, for example,
Temperature fluctuations of
Planck Collaboration, arXiv://1502.01589
CMB bipectrum 3/28
Gaussian :
Non-Gaussian :
3-point function (Bispectrum)
Bispectrum gives the statistical properties beyond the power specttrum,
CMB bipectrum 4/28
... parameterised by
primordial generated by non-linearity
?inflation after inflation
Unfortunately dominant ...
How large ?
New inflationChaotic inflation
Power-law inflationDBI inflationK-inflation
Hybrid inflationMSSM inflationBrane inflation...
CMB bipectrum 5/28
Collision term ofThomson scattering(only for photons)
Matsubara, “Uchuron no Butsuri” (Tokyo Univ.)
Photon/Neutrino
CDM/Baryon
Photon's Thomson scatteringterm is derived from Boltzmann eq.of baryons.
Gravity
Boltzmann eqs.
Continuity/Euler eqs.
Perturbed Einstein eqs.
Photon polarisation Massless neutrino temperature
CMB bipectrum 7/28
Integral form of Boltzmann equation
Seljak, Zaldarriaga, APJ 469 (1996) 437
suppressed by tight-couplingbetween baryons-photons
COS (Lensing) 8.93(0) -2.97(-1) -2.89(+1) 4.45(+1)m309e
We, for the first time, justify the remapping approach as a scheme to estimatethe lensing effect. In the other words, thickness of LSS doesn't affect so much.
CMB bipectrum 21/28
A : Source or ISWB : GravitationalBispectra by tensor Curve-of-sight formula
Leading contributions
CMB bipectrum 22/28
Source x ISWSource x LensingSource x Time-delaySource x Deflection
ISW x ISW
ISW x Time-delayISW x Lensing
Source x ISWSource x LensingSource x Time-delaySource x Deflection
Source x ISWSource x LensingSource x Time-delaySource x Deflection
ISW x ISW
ISW x Time-delayISW x Lensing
ISW x Deflection
ISW x ISW
ISW x Time-delayISW x Lensing
ISW x Deflection
Totally,we have 7+7+7+8=29 kinds of fNL.
CMB bipectrum 23/28
(Single-template fitting)
m320c
PRELIMINARY
Local Equilateral Orthogonal Folded
Source x ISW -2.14(-1) 1.42(-2) 3.69(-1) -5.64(-1)
Source x Lensing -6.65(-1) 1.23(-1) 1.66(0) -2.52(0)
Source x Time-delay -3.68(-2) -1.17(-3) 5.27(-2) -8.17(-2)
Source x Deflection -1.53(-2) -5.50(-2) 1.39(-1) -2.34(-1)
ISW x ISW -1.75(-3) 1.58(-3) 9.20(-3) -1.36(-2)
ISW x Lensing -5.17(-3) -6.34(-3) 3.47(-2) -5.58(-2)
ISW x Time-delay 4.89(-2) 2.24(-3) -5.00(-2) 7.79(-2)
scalar tensor
CMB bipectrum 24/28
(Single-template fitting)
m320c
PRELIMINARY
Local Equilateral Orthogonal Folded
Source x ISW 3.38(-7) -3.32(-5) -1.34(-5) 8.46(-6)
Source x Lensing 1.09(-5) 2.71(-4) 2.31(-5) 6.40(-5)
Source x Time-delay 6.05(-5) 4.03(-5) -3.95(-5) 7.57(-5)
Source x Deflection 4.34(-9) -3.40(-5) -6.80(-6) -1.98(-6)
ISW x Lensing 1.32(-3) -3.09(-2) -2.45(-2) 2.65(-2)
ISW x Time-delay -1.12(-4) -3.53(-4) 1.57(-4) -3.72(-4)
ISW x Deflection -9.25(-5) 3.62(-3) 2.96(-3) -3.24(-3)
tensor scalar
CMB bipectrum 25/28
(Single-template fitting)
m320c
PRELIMINARY
Local Equilateral Orthogonal Folded
Source x ISW 1.16(-7) 6.96(-7) -4.67(-6) 7.47(-6)
Source x Lensing -8.31(-7) -1.97(-5) -3.01(-6) -2.59(-6)
Source x Time-delay -1.60(-5) -3.91(-7) 1.43(-5) -2.22(-5)
Source x Deflection 3.00(-7) 4.66(-5) 7.52(-6) 5.52(-6)
ISW x ISW -6.39(-5) -6.39(-4) 7.63(-4) -1.41(-3)
ISW x Lensing -7.64(-5) 1.36(-3) 1.02(-3) -1.07(-3)
ISW x Time-delay 1.39(-5) 5.79(-5) -1.77(-4) 2.94(-4)
ISW x Deflection 1.80(-5) -3.59(-3) -1.82(-3) 1.50(-3)
tensor tensor
CMB bipectrum 26/28
(Single-template fitting)
m320c
PRELIMINARY
Local Equilateral Orthogonal Folded
Scalar x Scalar 9.05(0) 1.46(0) -2.94(+1) 4.59(+1)
Scalar x Tensor -8.89(-1) 7.83(-2) 2.21(0) -3.39(0)
Tensor x Scalar 1.18(-3) -2.74(-2) -2.14(-2) 2.30(-2)
Tensor x Tensor -1.25(-4) -2.78(-3) -2.04(-4) -7.07(-4)
CMB bipectrum 27/28
New CMB Boltzmann code implemeting 'curve'-of-sight formulas
* 1st-order scalar and tensor are completed. (TT, TE, EE, BB)
* Different schemes from CAMB, but consistent within O(1)%
* Implemented “curve”-of-sight formulas (2nd-order line-of-sight) for scalar and tensor temperature fluctuations.