Extended tachyon field using form invariance symmetry

Abstract

In this work we illustrate how form-invariance transformations (FITs) can be used to construct phantom and complementary tachyon cosmologies from standard tachyon field universes. First we show how these transformations act on the Hubble expansion rate, and the energy density and pressure of the tachyon field. Then we use the FIT to generate three different families of the tachyon field. In other words, the FIT generates new cosmologies from a known ``seed'' one; in particular, we apply the FIT to the ordinary tachyon field to obtain two types of tachyon species, denoted as the phantom and complementary tachyons. We see that the FIT allows us to pass from a nonstable cosmology to a stable one and vice versa. Finally, as an example, we apply the transformations to an inverse-square potential, $V\ensuremath{\propto}{\ensuremath{\phi}}^{\ensuremath{-}2}$, and generate the extended tachyon field.