R² 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+αR²+βR² 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 4 × 10^-4≲ r≲0.03 and 0.94≲ n_s ≲ 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 n_s ∼ 1 or higher. Other inflationary observables are dn_s/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.