Dynamical System Analysis for Steep Potentials

Abstract

In this work we have performed the dynamical system analysis for steep(er) exponential potentials considering different values of the steepness index $n$. We have performed the analysis using centre manifold theory as well as by employing numerical method. We have shown that in most of the cases, the higher values of steepness index corresponds to an unstable solution. We have shown that with this steep(er) potentials one can not have a phase transition from dark matter to dark energy in the past.