Analytical Insights into Constant-Roll Condition: Extending the Paradigm to Non-Canonical Models

Abstract

In this work, we explore the prospect of generalizing the constant-roll condition in canonical inflationary model to non-canonical models. To find a natural generalization, we focus on three manifestations of this condition and construct constant-roll models corresponding to each manifestation. These models are not equivalent but reduce to the familiar constant-roll model in canonical limit. To showcase the applicability of our generalized mechanism, we examine a specific class of non-canonical models, which can be viewed as extensions of k/G inflation. In these models sound speed is constant. We conduct a comparative study, and with an analytical examination of the model, specify instances when our constant-roll conditions yield dissimilar outcomes and when they exhibit analogies. We also apply our findings to scrutinize another kinetically driven inflationary model with varying sound speed. We demonstrate that each of our constant-roll conditions leads to a unique set of solutions. Afterward, we construct a four-stage constant-roll kinetically driven inflation that complies with CMB constraints, it sustains for a sufficiently long period of time, and finally gracefully exits. In this model the spectrum of curvature perturbations is enhanced in a brief phase of non-slow-roll inflationary evolution. Employing numerical methods, we analyse this scenario to elucidate how altering the constant-roll condition impacts the power spectrum and the model's dynamics.