Distortion of quintessence dynamics by the generalized uncertainty principle

In this paper, we introduce the generalized uncertainty principle (GUP) into the symmetry-reduced cosmological Hamiltonian for a universe influenced by a quintessence scalar field with potential. Our investigation centers on the semi-classical regime. Specifically, we derive the GUP-modified versions of the Friedmann, Raychaudhuri, and Klein–Gordon equations. Subsequently, we conduct a systematic analysis of the qualitative dynamics for the potential $V\left(\varphi \right)=V_0{sinh}^{-n}\left(\mu \varphi \right)$. This involves formulating an autonomous dynamical system using suitable dynamical variables, followed by a qualitative analysis through linear stability theory. Our findings reveal that incorporating GUP markedly alters the fixed points compared to the scenario without quantum effects, where GUP is not considered.