Cosmological Evolution of the Rolling Tachyon

TL;DR

The paper addresses the cosmological evolution of a rolling tachyon coupled to gravity within an effective field theory framework. It adopts a Born-Infeld-type tachyon action with potential $V(T)$ and derives the FRW dynamics, obtaining $\rho = \frac{V(T)}{\sqrt{1-\dot T^2}}$, $P = -V(T)\sqrt{1-\dot T^2}$, and $w = -(1-\dot T^2)$ with $-1 \le w \le 0$, illustrating how tachyon condensation can drive expansion. As the tachyon rolls toward its ground state, the expansion persists but the acceleration eventually ceases due to increasing $\dot T$, with asymptotic outcomes depending on the spatial curvature: $k=0$ yields $a(t) \to \text{const}$ and $k=-1$ yields the Milne limit $a(t) \sim t$, while $k=+1$ re-collapses. The work highlights how a tachyon condensate can induce transient acceleration and lead to flat-space remnants, offering a concrete cosmological scenario distinct from pure supergravity models and contributing to the broader exploration of tachyon cosmology and open string dynamics in early- and late-time Universe evolution.

Abstract

The cosmological effects of the tachyon rolling down to its ground state are discussed by coupling a simple effective field theory for the tachyon field to Einstein gravity. As the tachyon rolls down to the minimum of its potential the universe expands. Depending upon initial conditions, the scale factor may or may not start off accelerating, but ultimately it ceases to do so and the final flat spacetime is either static in the rest frame of the tachyon (if $k=0$) or (if $k=-1$) given by the Milne model.