$R^2\log R$ quantum corrections and the inflationary observables

Abstract

We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is $f(R)=R+\alpha R^2+\beta R^2\ln R$. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index $n_s$ and the tensor to scalar ratio yield $10^{-4}\lesssim r\lesssim 0.03$ and $0.94\lesssim n_s\lesssim 0.99$. i.e. $r$ is an order of magnitude bigger or smaller than the original Starobinsky model which predicted $r\sim 10^{-3}$. Further enhancement of $r$ gives a scale invariant $n_s\sim 1$ or higher. Other inflationary observables are $d{n}_s/d\ln k\gtrsim -5.2\times 10^{-4},\mu \lesssim 2.1\times 10^{-8},y\lesssim 2.6\times 10^{-9}$. Despite the enhancement in $r$, if the recent BICEP2 measurement stands, this model is disfavoured.

Comments: LaTeX, 9+1 pages, 5 figures