Brane world models with bulk perfect fluid and broken 4D Poincare invariance

TL;DR

This paper explores 5D brane world models with broken 4D Poincaré invariance, analyzing bulk perfect fluids and singularities, and presents regular solutions including generalizations of the Randall-Sundrum model.

Contribution

It introduces new exact solutions for brane models with bulk perfect fluids, including cases with broken and restored 4D Poincaré invariance, extending previous models.

Findings

Regular solutions for two-brane models with singularities cut off.

Analytic solutions for specific bulk perfect fluid equations of state.

Generalization of the Randall-Sundrum model with anisotropic bulk fluid.

Abstract

We consider 5D brane world models with broken global 4D Poincar\a'{e} invariance (4D part of the spacetime metric is not conformal to the Minkowski spacetime). The bulk is filled with the negative cosmological constant and may contain a perfect fluid. In the case of empty bulk (the perfect fluid is absent), it is shown that one brane solution always has either a physical or a coordinate singularity in the bulk. We cut off these singularities in the case of compact two brane model and obtain regular exact solutions for both 4D Poincar\a'{e} broken and restored invariance. When the perfect fluid is present in the bulk, we get the master equation for the metric coefficients in the case of arbitrary bulk perfect fluid equation of state (EoS) parameters. In two particular cases of EoS, we obtain the analytic solutions for thin and thick branes. First one generalizes the well known Randall-Sundrum model with one brane to the case of the bulk anisotropic perfect fluid. In the second solution, the 4D Poincar\a'{e} invariance is restored. Here, the spacetime goes asymptotically to the anti-de Sitter one far from the thick brane.