(R^2\log R\) quantum corrections and the inflationary observables

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.