Crossing the phantom divide with k-essence in brane-worlds

TL;DR

This paper investigates a brane-world cosmology with k-essence fields, demonstrating conditions for crossing the phantom divide, and analyzing the resulting cosmic evolution including singularities, de Sitter phases, and big rip scenarios.

Contribution

It introduces a model of a flat 3-brane with k-essence and a cosmological constant, analyzing phantom divide crossing and cosmic evolution in high and low energy regimes.

Findings

Effective equation of state resembles a modified Chaplygin gas at high energy.

The universe can evolve from a singularity to a de Sitter phase or end in a big rip.

Conditions for phantom divide crossing are derived using energy conditions.

Abstract

We study a flat 3-brane in presence of a linear $k$ field with nonzero cosmological constant $\Lambda_{4}$. In this model the crossing of the phantom divide (PD) occurs when the $k$-essence energy density becomes negative. We show that in the high energy regime the effective equation of state has a resemblance of a modified Chaplygin gas while in the low energy regime it becomes linear. We find a scale factor that begins from a singularity and evolves to a de Sitter stable stage while other solutions have a super-accelerated regime and end with a big rip. We use the energy conditions to show when the effective equation of state of the brane-universe crosses the PD.