Dynamics of Tachyon and Phantom Field beyond the Inverse Square Potentials

TL;DR

This paper extends the analysis of tachyon and phantom-tachyon scalar fields' cosmological evolution by considering a variable potential parameter, revealing diverse potentials that produce similar universe dynamics beyond the inverse square potential.

Contribution

It introduces a three-dimensional dynamical system framework by allowing the potential parameter b3 to depend on bb, enabling analysis of more general potentials beyond the inverse square case.

Findings

Multiple potentials yield scaling and dominant solutions when b3(bb) = 3/2.

Different potentials can produce indistinguishable universe evolution dynamics.

The analysis extends the understanding of scalar field cosmology beyond traditional inverse square potentials.

Abstract

We investigate the cosmological evolution of the tachyon and phantom-tachyon scalar field by considering the potential parameter $\Gamma$($=\frac{V V"}{V'^2}$) as a function of another potential parameter $\lambda$($=\frac{V'}{\kappa V^{3/2}}$), which correspondingly extends the analysis of the evolution of our universe from two-dimensional autonomous dynamical system to the three-dimension. It allows us to investigate the more general situation where the potential is not restricted to inverse square potential and .One result is that, apart from the inverse square potential, there are a large number of potentials which can give the scaling and dominant solution when the function $\Gamma(\lambda)$ equals $3/2$ for one or some values of $\lambda_{*}$ as well as the parameter $\lambda_{*}$ satisfies condition Eq.(18) or Eq.(19). We also find that for a class of different potentials the dynamics evolution of the universe are actually the same and therefore undistinguishable.