R2 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+αR2+βR2 ln R. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index ns and the tensor to scalar ratio yield 4 × 10-4≲ r≲0.03 and 0.94≲ ns ≲ 0.99. i.e. r is an order of magnitude bigger or smaller than the original Starobinsky model which predicted r ∼ 10-3. Further enhancement of r gives a scale invariant ns ∼ 1 or higher. Other inflationary observables are dns/dln k ≳ -5.2 × 10-4, μ ≲ 2.1 × 10-8 , y ≲ 2.6 × 10-9. Despite the enhancement in r, if the recent BICEP2 measurement stands, this model is disfavoured.