Extended tachyon field using form invariance symmetry

TL;DR

This paper demonstrates how form-invariance transformations can generate new stable or unstable tachyon cosmologies, including phantom and complementary types, from known solutions, exemplified by an inverse square potential.

Contribution

It introduces a method to construct extended tachyon cosmologies using form-invariance transformations, expanding the class of solutions beyond standard tachyon models.

Findings

Transformations relate different tachyon cosmologies, including phantom and complementary types.

They enable passing between stable and non-stable cosmological solutions.

Application to inverse square potential illustrates the generation of extended tachyon fields.

Abstract

In this work we illustrate how form-invariance transformations (FIT) can be used to construct phantom and complementary tachyon cosmologies from standard tachyon field universes. We show how these transformations act on the Hubble expansion rate, the energy density, and pressure of the tachyon field. The FIT generate new cosmologies from a known "seed" one, in particular from the ordinary tachyon field we obtain two types of tachyon species, denominated phantom and complementary tachyon. We see that the FIT allow us to pass from a non-stable cosmology to a stable one and vice-versa, as appeared in the literature. Finally, as an example, we apply the transformations to a cosmological fluid with an inverse square potential, $V \propto \phi^{-2}$, and generate the extended tachyon field.