6Ⅱ-6. Particle Physics

RIKEN Accel. Prog. Rep. 48 (2015)

Non-Gaussianities of primordial perturbations and tensor soundspeed†
T. Noumi∗1 and M. Yamaguchi∗2Inflation is now widely accepted as a paradigm ofearly Universe to explain the origin of the primordial
perturbations as well as to solve the horizon and theflatness problems of the standard big-bang cosmology.
The current observational data such as the cosmic microwave background (CMB) anisotropies support almost scale-invariant, adiabatic, and Gaussian primordial curvature fluctuations as predicted by inflation.
While the paradigm itself is well established and widelyaccepted, its detailed dynamics, e.g. the identificationof an inflaton, its kinetic and potential structure, andits gravitational coupling, are still unknown.
The non-Gaussianities of primordial curvature perturbations are powerful tools to give such informations.
For example, it is well-known that the equilateral typeof bispectrum of primordial curvature perturbations isenhanced by the inverse of their sound speed squared1,2). The null observation of the equilateral type byequil= 42 ± 75
the Planck satellite, characterized as fNL3)(68% CL) , yields stringent constraints on the soundspeed of the curvature perturbations as cs ≥ 0.02 (95%CL)3) .
Inflation generates not only primordial curvature
perturbations but also primordial tensor perturbations
4). Very recently, it was reported that primordial tensor perturbations have been found and the tensor-to5)
scalar ratio r is given by r = 0.20+0.07−0.05 (68% CL) ,though it is constrained as r < 0.11(95% CL) in
the Planck results6) . Their amplitude directly determines the energy scale of inflation, so it is estimated as V 1/4  2.2 × 1016 GeV given r  0.25) andPζ  2.2 × 10−96) . If we go beyond the powerspectrum, it is known that the bispectra of primordial tensor perturbations enable us to probe the gravitational
coupling of the inflaton field7) . Such a non-trivial gravitational coupling easily modifies the sound speed ofprimordial tensor perturbations, cγ , and it can significantly deviate from unity8) . Then, one may wonder ifthe small sound velocity of primordial tensor perturbations can enhance their non-Gaussianities as in thecase of the curvature perturbations. In this work, weaddressed this issue.
The relation between the sound speed and thenon-Gaussianities of primordial curvature perturbations can be clearly understood by use of the effective field theory (EFT) approach to inflation9) . Inflation can be characterized by the breakdown of timediffeomorphism invariance due to the time-dependent†∗1∗2

cosmological background and the general action for
inflation can be constructed based on this symmetry
breaking structure. The primordial curvature perturbation can be identified with the Goldstone mode π associated with the breaking of time-diffeomorphism invariance. The symmetry arguments require that modification of the sound speed cs induces non-negligible
cubic interactions of the Goldstone mode π, and hence
the sound speed and the bispectrum of the curvature
perturbations are directly related.
In this work, we investigated the relation between
the sound speed of tensor perturbations and the bispectrum of primordial perturbations, based on theEFT approach. We first identified what kind of operators can modify the tensor sound speed. Then, weclarify which type of non-Gaussianity arises associatedwith the modification and can be used as a probe forthe tensor sound speed. We found that the tensor
sound speed is not directly related to tensor bispectra,in contrast to the scalar sound speed case. We also
discussed primordial trispectra as a possible probe oftensor sound speed.
References
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Condensed from the article in arXiv:1403.6065.
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