Noether Symmetry Approach in f(R) Tachyon Model

TL;DR

This paper employs the Noether symmetry approach to derive specific forms of the tachyon potential and f(R) functions in a flat FRW cosmology, revealing a power-law f(R) and inverse fourth power tachyon potential, and explores their cosmological implications.

Contribution

It introduces a method to determine the tachyon potential and f(R) functions using Noether symmetry, providing new exact solutions in f(R) tachyon cosmology.

Findings

Power-law f(R) function obtained

Inverse fourth power tachyon potential derived

Cosmological evolution shows crossing of the equation of state boundary

Abstract

In this Letter by utilizing the Noether symmetry approach in cosmology, we attempt to find the tachyon potential via the application of this kind of symmetry to a flat Friedmann-Robertson-Walker (FRW) metric. We reduce the system of equations to simpler ones and obtain the general class of the tachyon's potential function and $f(R)$ functions. We have found that the Noether symmetric model results in a power law $f(R)$ and an inverse fourth power potential for the tachyonic field. Further we investigate numerically the cosmological evolution of our model and show explicitly the behavior of the equation of state crossing the cosmological constant boundary.