Modelling Tachyon Cosmology with Non-Minimal Derivative Coupling to Gravity

TL;DR

This paper investigates a tachyon cosmological model with non-minimal derivative coupling to gravity, deriving conditions for accelerated expansion and simplifying the equations through special redefinitions and integrals.

Contribution

It introduces a novel redefinition of the tachyon field and derives first integrals that simplify the analysis of non-minimally coupled tachyon cosmology.

Findings

Derived conditions for accelerated expansion in the model

Obtained effective energy density and pressure expressions

Simplified equations via special redefinitions and integrals

Abstract

We study a tachyon model with non-minimal derivative coupling to gravity in the Friedmann-Robertson-Walker flat cosmology. We propose the special re-definition of the tachyon field which allows us to represent tachyon field equation formally coinciding with its usual form but with re-defined Hubble parameter. Two first integrals for the model equations are obtained that can essentially simplify both further analysis and analytical solving for the model. These integrals become the trivial identities in the case of minimal coupling. The effective energy density and pressure of the tachyon field are obtained, and the necessary condition of the possibility for this model to expand with acceleration is derived.