Late acceleration and $w=-1$ crossing in induced gravity

TL;DR

This paper investigates the cosmological evolution of a brane universe with induced gravity in a bulk with arbitrary matter, revealing how dark radiation influences expansion and causes a crossing of the phantom divide.

Contribution

It derives effective Friedmann equations for a brane with induced gravity, showing the impact of bulk matter and dark radiation on cosmic acceleration and dark energy behavior.

Findings

Hubble rate depends on bulk's integrated mass and dark radiation.

Two solution branches with different cosmological behaviors.

Dark radiation can induce acceleration and phantom divide crossing.

Abstract

We study the cosmological evolution on a brane with induced gravity within a bulk with arbitrary matter content. We consider a Friedmann-Robertson-Walker brane, invariantly characterized by a six-dimensional group of isometries. We derive the effective Friedmann and Raychaudhuri equations. We show that the Hubble expansion rate on the brane depends on the covariantly defined integrated mass in the bulk, which determines the energy density of the generalized dark radiation. The Friedmann equation has two branches, distinguished by the two possible values of the parameter $\ex=\pm 1$. The branch with $\ex=1$ is characterized by an effective cosmological constant and accelerated expansion for low energy densities. Another remarkable feature is that the contribution from the generalized dark radiation appears with a negative sign. As a result, the presence of the bulk corresponds to an effective negative energy density on the brane, without violation of the weak energy condition. The transition from a period of domination of the matter energy density by non-relativistic brane matter to domination by the generalized dark radiation corresponds to a crossing of the phantom divide $w=-1$.