Abstract
If the graviton is the only high spin particle present during inflation, then the form of the observable tensor three-point function is fixed by de Sitter symmetry at leading order in slow-roll, regardless of the theory, to be a linear combination of two possible shapes. This is because there are only a fixed number of possible on-shell cubic structures through which the graviton can self-interact. If additional massive spin-2 degrees of freedom are present, more cubic interaction structures are possible, including those containing interactions between the new fields and the graviton, and self-interactions of the new fields. We study, in a model-independent way, how these interactions can lead to new shapes for the tensor bispectrum. In general, these shapes cannot be computed analytically, but for the case where the only new field is a partially massless spin-2 field we give simple expressions. It is possible for the contribution from additional spin-2 fields to be larger than the intrinsic Einstein gravity bispectrum and provides a mechanism for enhancing the size of the graviton bispectrum relative to the graviton power spectrum.
Highlights
A generic prediction of inflation is a nearly Gaussian spectrum of primordial tensor perturbations, arising from fluctuations of the graviton about the nearly de Sitter inflationary background
There is a certain universality in these objects; in the de Sitter limit, their form is completely fixed by conformal invariance up to a finite number of constants [73], much as the structure of three-point on-shell scattering amplitudes is fixed by Lorentz invariance [74]
We have studied the imprints of massive spin-2 fields on inflationary tensor nonGaussianities
Summary
A generic prediction of inflation is a nearly Gaussian spectrum of primordial tensor perturbations, arising from fluctuations of the graviton about the nearly de Sitter inflationary background. We perform a model-independent study of the possible new shapes of tensor non-Gaussianity that can arise due to the presence of additional heavy spin-2 fields We do this by classifying the possible on-shell cubic vertices through which a massive spin-2 field can interact with itself and with the graviton. There has been great progress recently both in systematizing the computation of correlation functions in cosmology using de Sitter symmetry [2, 51, 53,54,55,56,57,58,59] and in the related problem of studying conformal field theories in momentum space [60,61,62,63] To this point, investigations involving external fields with spin have focused on the massless cases, where gauge invariance (or current conservation) provides numerous simplifications. We focus on the imprint that partially massless fields can leave on the graviton bispectrum γ3
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