What is needed of a tachyon if it is to be the dark energy?

TL;DR

This paper investigates the conditions under which a tachyon field can drive late-time cosmic acceleration, analyzing different asymptotic behaviors of the potential's parameter and their implications for dark energy models.

Contribution

It provides a detailed analysis of the dynamical behavior of tachyon fields with various potential asymptotics and their viability as dark energy candidates.

Findings

Constant λ leads to late-time acceleration with inverse square potential.

Asymptotically zero λ allows for a dynamic approach to an evolving critical point.

Large |λ| prevents late-time acceleration but may produce transient acceleration.

Abstract

We study a dark energy scenario in the presence of a tachyon field $\phi$ with potential $V(\phi)$ and a barotropic perfect fluid. The cosmological dynamics crucially depends on the asymptotic behavior of the quantity $\lambda=-M_pV_\phi/V^{3/2}$. If $\lambda$ is a constant, which corresponds to an inverse square potential $V(\phi) \propto \phi^{-2}$, there exists one stable critical point that gives an acceleration of the universe at late times. When $\lambda \to 0$ asymptotically, we can have a viable dark energy scenario in which the system approaches an ``instantaneous'' critical point that dynamically changes with $\lambda$. If $|\lambda|$ approaches infinity asymptotically, the universe does not exhibit an acceleration at late times. In this case, however, we find an interesting possibility that a transient acceleration occurs in a regime where $|\lambda|$ is smaller than of order unity.