Dynamical evolution of quintessence cosmology in a physical phase space

TL;DR

This paper analyzes the dynamical evolution of quintessence cosmology using phase space methods, revealing transient acceleration and addressing the limitations of differential equations with a numerical approach.

Contribution

It introduces a phase space analysis for quintessence cosmology with exponential potential, showing transient acceleration and improving the understanding of scalar field equations.

Findings

Current universe state can be pinpointed in phase diagrams

Scaling solutions can induce transient acceleration

Numerical methods address incomplete differential equations

Abstract

The phase space analysis of cosmological parameters $\Omega_{\phi}$ and $\gamma_{\phi}$ is given. Based on this, the well-known quintessence cosmology is studied with an exponential potential $V(\phi)=V_{0}\exp(-\lambda\phi)$. Given observational data, the current state of universe could be pinpointed in the phase diagrams, thus making the diagrams more informative. The scaling solution of quintessence usually is not supposed to give the cosmic accelerating expansion, but we prove it could educe the transient acceleration. We also find that the differential equations of system used widely in study of scalar field are incomplete, and then a numerical method is used to figure out the range of application.