Accelerated expansion of the universe driven by tachyonic matter

TL;DR

The paper investigates whether any prescribed cosmic expansion history a(t) can be realized in a flat FRW cosmology using either a normal scalar field or a tachyonic field by reconstructing the corresponding potential V(φ). It provides explicit formulas linking H, φ, and V for both cases and illustrates with analytic examples that yield exponential and inverse-square potentials, highlighting a close link between the two formulations. The results show that tachyon condensates can mimic a cosmological constant or contribute to the late-time acceleration under certain asymptotic conditions, while also offering applications to early-universe inflation and string-theory constraints on φ̇(∞). The work thus offers a practical, model-agnostic framework to interpret observed expansion histories within scalar and tachyonic field theories and to explore string-theoretic cosmologies.

Abstract

It is an accepted practice in cosmology to invoke a scalar field with potential $V(φ)$ when observed evolution of the universe cannot be reconciled with theoretical prejudices. Since one function-degree-of-freedom in the expansion factor $a(t)$ can be traded off for the function $V(φ)$, it is {\it always} possible to find a scalar field potential which will reproduce a given evolution. I provide a recipe for determining $V(φ)$ from $a(t)$ in two cases:(i) Normal scalar field with Lagrangian ${\cal L} = (1/2)\partial_aφ\partial^aφ- V(φ)$ used in quintessence/dark energy models. (ii) A tachyonic field with Lagrangian ${\cal L} = -V(φ) [ 1- \partial_aφ\partial^aφ]^{1/2} $, motivated by recent string theoretic results. In the latter case, it is possible to have accelerated expansion of the universe during the late phase in certain cases. This suggests a string theory based interpretation of the current phase of the universe with tachyonic condensate acting as effective cosmological constant.