A Smooth Constant-Roll to a Slow-Roll Modular Inflation Transition

TL;DR

This paper explores a smooth transition from constant-roll to slow-roll inflation within a scalar field framework, revealing that the transition can occur with fewer e-foldings and allows for graceful exit, enhancing understanding of inflationary dynamics.

Contribution

It demonstrates a novel smooth transition mechanism between constant-roll and slow-roll inflation, including conditions for stability and compatibility with modular inflationary potentials.

Findings

Transition can occur with fewer e-foldings than traditionally assumed.

Graceful exit from inflation is possible after the transition.

Stable attractors exist, ensuring a consistent dynamical evolution.

Abstract

In this work, we investigate how a smooth transition from a constant-roll to a slow-roll inflationary era may be realized, in the context of a canonical scalar field theory. We study in some detail the dynamical evolution of the cosmological system, and we investigate whether a stable attractor exists, both numerically and analytically. We also investigate the slow-roll era and as we demonstrate, partially compatibility of the resulting scalar theory, may be achieved, with the potential of the latter belonging to a class of modular inflationary potentials. The novel features of the constant-roll to slow-roll transition which we achieved, are firstly that the it is not compelling for the slow-roll era to last for $N\sim 50-60$ $e$-foldings, but it may last for a smaller number of $e$-foldings, since some $e$-foldings may occur during the constant-roll era. Secondly, when the slow-roll era occurs after the constant-roll era, the graceful exit from inflation may occur, a feature absent in the constant-roll scenario, due to the stability properties of the final attractor in the constant-roll case.