Attractor Solution of Phantom Field

TL;DR

This paper studies the late-time behavior of a phantom dark energy model with an exponential potential, showing it has a stable attractor solution that addresses fine-tuning issues and determines the equation of state.

Contribution

It demonstrates the existence of a stable attractor in the phantom field model with exponential potential, providing insights into dark energy dynamics and stability.

Findings

Existence of a late-time attractor solution.

Equation of state $w$ depends on the potential parameter $\lambda$.

Model stability for current observable universe.

Abstract

In light of recent study on the dark energy models that manifest an equation of state $w<-1$, we investigate the cosmological evolution of phantom field in a specific potential, exponential potential in this paper. The phase plane analysis show that the there is a late time attractor solution in this model, which address the similar issues as that of fine tuning problems in conventional quintessence models. The equation of state $w$ is determined by the attractor solution which is dependent on the $\lambda$ parameter in the potential. We also show that this model is stable for our present observable universe.