Constant-Roll (Quasi-)Linear Inflation

In constant-roll inflation, the scalar field that drives the accelerated expansion of the Universe is rolling down its potential at a constant rate. Within this framework, we highlight the relations between the Hubble slow-roll parameters and the potential ones, studying in detail the case of a single-field Coleman-Weinberg model characterised by a non-minimal coupling of the inflaton to gravity. With respect to the exact constant-roll predictions, we find that assuming an approximate slow-roll behaviour yields a difference of $\Delta r = 0.001$ in the tensor-to-scalar ratio prediction. Such a discrepancy is in principle testable by future satellite missions. As for the scalar spectral index $n_s$, we find that the existing 2-$\sigma$ bound constrains the value of the non-minimal coupling to $\xi_\phi \sim 0.29-0.31$ in the model under consideration.