k-essence and tachyons in brane-worlds

TL;DR

This paper explores the dynamics of k-essence and tachyon fields on branes, revealing diverse cosmological behaviors including bouncing, collapsing, and singularity-driven evolutions, and examines the limitations of atypical models.

Contribution

It introduces a comprehensive analysis of linear and nonlinear k-essence models in brane-world cosmology, including the behavior of extended tachyonic fields and their high/low energy limits.

Findings

Solutions include expanding, contracting, and bouncing universes.

Atypical k-essence models are dynamically incomplete.

Universe evolves between two singularities with negative energy tachyon fields.

Abstract

We investigate a k-essence field localized on the brane evolving linearly with the cosmological time for arbitrary kinetic functions and consider the atypical k-essence model for linear and nonlinear k-fields in Friedmann-Robertson-Walker (FRW) cosmology. In the former case the k-field is driven by an inverse quadratic polynomial potential and the solutions exhibit several different behaviors which include expanding, contracting and bouncing universes as well as a model with a finite time span, some of them ending in a big crunch or a big rip. In the latter case we find the potential and show that the atypical k-essence model is dynamically uncomplete. Particularly, by selecting the extended tachyonic kinetic functions we analyze the high and low energy limits of our model, obtaining the nearly power law solution. We introduce a tachyon field with negative energy density and show that the universe evolves between two singularities.