Non-local Starobinsky inflation in the light of future CMB

Abstract

Analytic infinite derivative (AID) non-local quadratic curvature gravity in Weyl basis is known to be ghost free, superrenormalizable or finite and perturbatively Unitary and as such it is Ultra-Violet (UV) complete. Recently $R+R^2$ ("Starobinsky") inflation was successfully embedded in AID non-local gravity and the corresponding observables were computed. Here in this paper, we derive the form factors compatible within near de Sitter aproaximation and prove that the theory must contain a scalaron that drives inflationary expansion. Further more we consider the form factors (AID non-local operators) proposed by Tomboulis in hep-th/9702146 and compute the corresponding predictions of tensor to scalar ratio and tensor tilt $\left( n_t,\,r \right)$ where the scalar tilt remains the same as the local Starobinsky model. Anticipating future CMB probes such will be able to test non-local Starobinsky inflation we constrain the scale of non-locality to be $10^{14}\,GeV\lesssim\mathcal{M}\lesssim 5\times 10^{14}\,GeV$ and $10^{-7}\lesssim r \lesssim 0.07$ for different form factors. We found that it possible to have a blue or red tensor tilt $\left( n_t\gtrless 0 \right)$ depending on the scale of non-locality and the form factor. We also comment on Higgs inflation in non-local context.