Inflationary models that generalize the constant roll constraint

TL;DR

This paper extends constant roll inflation models by introducing a broader class of constraints, finding exact solutions with potentials compatible with observational data on spectral index and tensor-to-scalar ratio.

Contribution

It generalizes previous constant roll models by deriving exact solutions for a wider class of constraints and demonstrates their observational viability.

Findings

Exact solutions without initial singularity

Models consistent with current observational data

Potential functions with periodic cosine terms

Abstract

Recently a class of inflationary models satisfying the constant rate of roll constraint, $\ddot{\phi}+(3+\alpha)H\dot{\phi}=0$, has been studied and compared with the latest cosmological observational data. We consider the broader class of constraints $ \ddot{\phi}+\frac{\alpha_1}{2}\dot{\phi}+\alpha_2 H\dot{\phi}=0$ and find an exact particular solution, without initial singularity, which is an attractor of the dynamics governed by a positive periodic potential $V(\phi)=E+ F \cos (\Omega \phi )+G \cos (2 \Omega \phi )$. The spectral index $n_s$ and the tensor to scalar ratio $r$ are consistent with the recent observational data.