Non-Gaussianities and tensor-to-scalar ratio in non-local R2-like inflation

Abstract

In this paper we will study R 2-like inflation in a non-local modification of gravity which contains quadratic in Ricci scalar and Weyl tensor terms with analytic infinite derivative form-factors in the action. It is known that the inflationary solution of the local R + R 2 gravity remains a particular exact solution in this model. It was shown earlier that the power spectrum of scalar perturbations generated during inflation in the non-local setup remains the same as in the local R + R 2 inflation, whereas the power spectrum of tensor perturbations gets modified due to the non-local Weyl tensor squared term. In the present paper we go beyond 2-point correlators and compute the non-Gaussian parameter f NL related to 3-point correlations generated during inflation, which we found to be different from those in the original local inflationary model and scenarios alike based on a local gravity. We evaluate non-local corrections to the scalar bi-spectrum which give non-zero contributions to squeezed, equilateral and orthogonal configurations. We show that f NL ∼ O(1) with an arbitrary sign is achievable in this model based on the choice of form-factors and the scale of non-locality. We present the predictions for the tensor-toscalar ratio, r, and the tensor tilt, n t. In contrast to standard inflation in a local gravity, here the possibility n t > 0 is not excluded. Thus, future CMB data can probe non-local behaviour of gravity at high space-time curvatures.

Predictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term

“…Inflation has been considered in nonlocal theories of gravity as well [40], where the classical action contains infinitely many free parameters. The cosmological perturbations in those scenarios have been studied in [41,42].…”

Non-unitarity of Minkowskian non-local quantum field theories

“…In facts, it has been shown that the model has a satisfactory Starobinsky-like inflation [32,33]. The spectrum of scalar perturbations generated during inflation is the same as in the local R 2 inflation [82], while tensor perturbations are affected by the non-locality [34][35][36]; indeed, NLQG is predictive.…”

Unattainability of the trans-Planckian regime in nonlocal quantum gravity

“…In particular, it has been shown that the Minkowski spacetime is stable under any Strongly Asymptotically Flat (SAF) initial data set satisfying a Global Smallness Assumption (GSA) [29], as in general relativity. Moreover, the model has a satisfactory Starobinsky-like inflation [52,53], and the spectrum of JHEP09(2020)056 scalar perturbations generated during inflation is the same as in the local Starobinsky R 2 inflation [54], while the spectrum of tensor perturbations is affected by the nonlocality, see [55][56][57] for the details. Indeed, nonlocal gravity can be falsified by future measurements of tensor perturbations.…”