Tracking solutions in tachyon cosmology

TL;DR

This paper analyzes the dynamical behavior of a universe filled with tachyonic and barotropic fluids using phase-plane methods, identifying fixed points and their stability to understand late-time cosmological evolution.

Contribution

It provides a detailed phase-plane analysis of tachyon cosmology with inverse square potential, revealing conditions for fluid dominance and stability of solutions.

Findings

Tachyonic fluid can dominate at late times if the barotropic fluid redshifts quickly.

Fixed-point solutions include attractors with different fluid dominance scenarios.

Residual tachyon contribution is constrained by nucleosynthesis requirements.

Abstract

We perform a thorough phase-plane analysis of the flow defined by the equations of motion of a FRW universe filled with a tachyonic fluid plus a barotropic one. The tachyon potential is assumed to be of inverse square form, thus allowing for a two-dimensional autonomous system of equations. The Friedmann constraint, combined with a convenient choice of coordinates, renders the physical state compact. We find the fixed-point solutions, and discuss whether they represent attractors or not. The way the two fluids contribute at late-times to the fractional energy density depends on how fast the barotropic fluid redshifts. If it does it fast enough, the tachyonic fluid takes over at late times, but if the opposite happens, the situation will not be completely dominated by the barotropic fluid; instead there will be a residual non-negligible contribution from the tachyon subject to restrictions coming from nucleosynthesis.