Prospects and Problems of Tachyon Matter Cosmology

TL;DR

The paper analyzes FRW cosmologies driven by tachyon matter described by a Dirac–Born–Infeld–type action, focusing on two string-theory–motivated potentials. For a finite minimum, the tachyon condensate oscillates with a negative pressure and a time-averaged equation of state, but linear fluctuations undergo exponential growth due to parametric resonance, signaling rapid decay of the condensate. For a runaway minimum, the tachyon behaves as pressureless matter with ε ∝ a^{-3}, and linear tachyon–gravity fluctuations exhibit CDM-like growth, though the linear regime ends quickly and non-linear dynamics must be addressed. Overall, the work highlights rich tachyon-based cosmologies with stability and clustering challenges, suggesting nonlinear and possibly higher-dimensional analyses are needed to assess viability as dark energy or dark matter.

Abstract

We consider the evolution of FRW cosmological models and linear perturbations of tachyon matter rolling towards a minimum of its potential. The tachyon coupled to gravity is described by an effective 4d field theory of string theory tachyon. In the model where a tachyon potential $V(T)$ has a quadratic minimum at finite value of the tachyon field $T_0$ and $V(T_0)=0$, the tachyon condensate oscillates around its minimum with a decreasing amplitude. It is shown that its effective equation of state is $p=-ε/3$. However, linear inhomogeneous tachyon fluctuations coupled to the oscillating background condensate are exponentially unstable due to the effect of parametric resonance. In another interesting model, where tachyon potential exponentially approaches zero at infinity of $T$, rolling tachyon condensate in an expanding universe behaves as pressureless fluid. Its linear fluctuations coupled with small metric perturbations evolve similar to these in the pressureless fluid. However, this linear stage changes to a strongly non-linear one very early, so that the usual quasi-linear stage observed at sufficiently large scales in the present Universe may not be realized in the absence of the usual particle-like cold dark matter.

Figures (3)

• Figure 1: Tachyon matter potentials with minima at finite (a) and infinite (b) values of the field. The potentials near minimum are taken to be: (a) $V(T) = \frac{1}{2} m^2 (T-T_0)^2$, (b) $V(T) = V_0 e^{-T/T_0}$.
• Figure 2: (a) Background tachyon oscillations in the model with $V(T) = \frac{1}{2} m^2 (T-T_0)^2$. (b) Background oscillations of tachyon equation of state. Constant horizontal line $\frac{p}{\varepsilon} = -\frac{1}{3}$ is the time-averaged equation of state.
• Figure 3: Instability of fluctuations $T_k(t)$ in the model with quadratic potential (scales are linear).