Generalized uncertainty principle distorted quintessence dynamics

Abstract

In this paper, we invoke a generalized uncertainty principle (GUP) in the symmetry-reduced cosmological Hamiltonian for a universe driven by a quintessence scalar field with potential. Our study focuses on semi-classical regime. In particular, we derive the GUP-distorted Friedmann, Raychaudhuri, and the Klein-Gordon equation. This is followed by a systematic analysis of the qualitative dynamics for the choice of potential $V(\phi)= V_0 \sinh^{-n}{(\mu \phi)}$. This involves constructing an autonomous dynamical system of equations by choosing appropriate dynamical variables, followed by a qualitative study using linear stability theory. Our analysis shows that incorporating GUP significantly changes the existing fixed points compared to the limiting case without quantum effects by switching off the GUP.