Non-Gaussianities and tensor-to-scalar ratio in non-local R ²-like inflation

In this paper we will study R²-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 + R² 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 + R² 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-to-scalar 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.