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

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.