Non-Gaussianities and tensor-to-scalar ratio in non-local $R^{2}$-like
  inflation
  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 $f_{NL}\sim
O(1)$ 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.
