Regular braneworlds with bulk fluids

TL;DR

This paper reviews the structure of regular braneworld solutions with bulk fluids, highlighting conditions for gravity localization and introducing nonlinear equations of state to improve solution properties.

Contribution

It identifies specific EoS parameters for regular solutions and proposes a nonlinear bulk fluid component to achieve finite Planck mass and singularity-free models.

Findings

Regular solutions exist for specific EoS parameters.

Only flat branes with EoS parameter -1 localize gravity.

Introducing nonlinear EoS improves solution regularity.

Abstract

We review studies on the singularity structure and asymptotic analysis of a 3-brane (flat or curved) embedded in a five-dimensional bulk filled with a `perfect fluid' with an equation of state with the `pressure' and the `density' of the fluid depending on the fifth space coordinate. Regular solutions satisfying positive energy conditions in the bulk exist only in the cases of a flat brane with an EoS parameter equal to -1, or of AdS branes for EoS parameter values in suitable intervals. More cases can be found by gluing two regular branches of solutions at the position of the brane. However, only the case of a flat brane with an EoS parameter equal to -1 leads to finite Planck mass on the brane and thus localises gravity. In a more recent work, we showed that a way to rectify the previous findings and obtain a solution for a flat brane in a finite range of the EoS parameter, which is both free from finite-distance singularities and compatible with the physical conditions of energy and finiteness of four-dimensional Planck mass, is by introducing a bulk fluid component that satisfies a nonlinear equation of state.