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Abstract In [1], a most general higher curvature non-local gravity action was derived that admits a particular R 2-like inflationary solution predicting the spectral index of primordial scalar perturbations n s N ≈ 1 − 1 2 $$ {n}_s(N)\approx 1-\frac{1}{2} $$ , 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 f NL (k 1, k 2, k 3) mimicking several classes of scalar field models of inflation known in the literature. We obtain |f 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 $$ \left|\frac{d\ln {f}_{\textrm{NL}}}{d\ln k}\right|\lesssim 1 $$ . 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 R 2-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 R 2-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 R 2-like inflation, we obtain a robust geometric framework of inflation that can explain any detection of observable quantities related to scalar PNGs. |
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