General Brane Dynamics with R_{4} term in the Bulk

TL;DR

This paper explores how including the intrinsic curvature term in brane-world models affects the induced brane dynamics, leading to modifications of Einstein's equations, potential violations of energy conditions, and novel cosmological solutions with accelerated phases.

Contribution

It provides a comprehensive analysis of brane dynamics with the R_{4} term, revealing new cosmological behaviors and solutions not previously characterized.

Findings

Induced brane dynamics resemble Einstein gravity with a modified energy-momentum tensor.

Conventional general relativity can re-emerge during an initial cosmological era.

A new anisotropic cosmological solution exhibits an intermediate acceleration phase.

Abstract

A general analysis of the induced brane dynamics is performed when the intrinsic curvature term is included in the action. Such a term is known to cause dramatic changes and is generically induced by quantum corrections coming from the bulk gravity and its coupling with matter living on the brane. The induced brane dynamics is shown to be the usual Einstein dynamics coupled to a well defined modified energy-momentum tensor. In cosmology, conventional general relativity revives for an initial era whose duration depends on the value of the five-dimensional Planck mass. Violations of energy conditions may be possible, as well as matter inhomogeneities on the brane in (A)dS_{5} or Minkowski backgrounds. A new anisotropic cosmological solution is given in the above context. This solution, for a fine-tuned five-dimensional cosmological constant, exhibits an intermediate accelerating phase which is followed by an era corresponding to a 4D perfect fluid solution with no future horizons.