Dynamical Systems Approach to Non-Slow-Roll Inflationary Models

In this work, we systematically present a new dynamical systems approach to nonstandard inflationary processes as constant-roll inflation and ultraslow-roll inflation. Using the techniques presented in our work one can in general investigate the attractor nature of the inflationary models in the phase space. We have compactified the phase space coordinates, wherever necessary, and regulated the nonlinear differential equations, constituting the autonomous system of equations defining the dynamical system, at the cost of a new redefined time variable which is a monotonic increasing function of the standard time coordinate. We have shown that in most of the relevant cases the program is executable although the two time coordinates may show different durations of cosmological events. Our methods of analysis differs slightly in different models but we have always emphasized on the nature of the initial conditions leading to stable inflationary phases in different cases. We have provided a universal language in terms of which various nonstandard inflationary models can be studied.