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

TL;DR

This paper explores an inflationary model with quantum-corrected R^2 terms, predicting a range of tensor-to-scalar ratios and spectral indices, but faces challenges aligning with recent BICEP2 results.

Contribution

It introduces a modified inflationary model with logarithmic R^2 corrections from quantum effects, analyzing its impact on observable parameters.

Findings

Tensor-to-scalar ratio r ranges from 10^{-4} to 0.03

Spectral index n_s varies between 0.94 and 0.99

Model is disfavoured if BICEP2 results are confirmed

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 $10^{-4}\lesssim r\lesssim0.03$ 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.