Non-Gaussianities in generalized non-local $R^2$-like inflation

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 $n_s(N)\approx 1-\frac{2}{N}$, where $N$ is the number of e-folds before the end of inflation, $N\gg 1$, 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 $f_{\mathrm{NL}}\left(k_1,k_2,k_3\right)$ mimicking several classes of scalar field models of inflation known in the literature. We obtain $|f_{\mathrm{NL}}|\sim O(1-10)$ in the equilateral, orthogonal, and squeezed limits and the running of these PNGs measured by the quantity $|\frac{d\ln f_{\mathrm{NL}}}{d\ln k}|\lesssim 1$. 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.

arXiv comment31 pages, 7 figures, discussions are improved, the abstract is slightly extended, matches with the version published in JHEP

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