Study Of Tachyon Dynamics For Broad Classes of Potentials

TL;DR

This paper analyzes the asymptotic behavior of tachyon cosmology across various potentials, revealing universal phase space features and classifying late-time attractors such as de Sitter and matter-scaling solutions.

Contribution

It introduces a generalized dynamical systems approach for tachyon models with broad potentials, extending previous methods and identifying universal equilibrium points.

Findings

Matter-dominated and ultra-relativistic solutions are always equilibrium points.

De Sitter solutions are late-time attractors for inverse power-law potentials.

Late-time behavior varies with potential type, including inflationary and matter-scaling phases.

Abstract

We investigate in detail the asymptotic properties of tachyon cosmology for a broad class of self-interaction potentials. The present approach relies in an appropriate re-definition of the tachyon field, which, in conjunction with a method formerly applied in the bibliography in a different context, allows to generalize the dynamical systems study of tachyon cosmology to a wider class of self-interaction potentials beyond the (inverse) square-law one. It is revealed that independent of the functional form of the potential, the matter-dominated solution and the ultra-relativistic (also matter-dominated) solution, are always associated with equilibrium points in the phase space of the tachyon models. The latter is always the past attractor, while the former is a saddle critical point. For inverse power-law potentials $V\propto\phi^{-2\lambda}$ the late-time attractor is always the de Sitter solution, while for sinh-like potentials $V\propto\sinh^{-\alpha}(\lambda\phi)$, depending on the region of parameter space, the late-time attractor can be either the inflationary tachyon-dominated solution or the matter-scaling (also inflationary) phase. In general, for most part of known quintessential potentials, the late-time dynamics will be associated either with de Sitter inflation, or with matter-scaling, or with scalar field-dominated solutions.