k-essence in the DGP brane-world cosmology

TL;DR

This paper investigates the dynamics of a DGP brane-world cosmology filled with a k-essence field, analyzing its behavior across different energy regimes and identifying various possible cosmic evolutions and singularities.

Contribution

It provides an analytical solution to the Friedmann equation in this setup and explores the diverse asymptotic behaviors of the brane, including acceleration and singularities.

Findings

Different asymptotic behaviors including acceleration, big bang, big crunch, big rip, and quiescent singularities.

Analytical solutions for the Friedmann equation in the DGP brane with k-essence.

Identification of sudden singularities in the model.

Abstract

We analyse a DGP brane filled with a k-essence field and assume the k-field evolving linearly with the cosmic time of the brane. We then solve analytically the Friedmann equation and deduce the different behaviour of the brane at the low and the high energy regimes. The asymptotic behaviour can be quite different involving accelerating branes, big bangs, big crunches, big rips or quiescent singularities. The latter correspond to a type of sudden singularity.