Non-Gaussianities in generalized non-local R²-like inflation

In [1], a most general higher curvature non-local gravity action was derived that admits a particular R²-like inflationary solution predicting the spectral index of primordial scalar perturbations 𝑛_𝑠(𝑁) ≈ 1 − ½, where N is the number of e-folds before the end of inflation, N ≫ 1, any value of the tensor-to-scalar ratio r(N) < 0.036 and the tensor tilt n_t(N) violating the r = –8n_t condition. In this paper, we compute scalar primordial non-Gaussianities (PNGs) in this theory and effectively demonstrate that higher curvature non-local terms lead to reduced bispectrum ƒ_NL (k₁, k₂, k₃) mimicking several classes of scalar field models of inflation known in the literature. We obtain |ƒ_NL| ~ O(1 – 10) in the equilateral, orthogonal, and squeezed limits and the running of these PNGs measured by the quantity |𝑑 ln ⁡𝑓_NL 𝑑 ln⁡ 𝑘| ≲ 1. Such PNGs are sufficiently large to be measurable by future CMB and Large Scale Structure observations, thus providing a possibility to probe the nature of quantum gravity. Furthermore, we demonstrate that the R²-like inflation in non-local modification of gravity brings non-trivial predictions which go beyond the current status of effective field theories (EFTs) of single field, quasi-single field and multiple field inflation. A distinguishable feature of non-local R²-like inflation compared to local EFTs is that we can have running of PNGs at least an order of magnitude higher. In summary, through our generalized non-local R²-like inflation, we obtain a robust geometric framework of inflation that can explain any detection of observable quantities related to scalar PNGs.