Brane world in Non-Riemannian Geometry

TL;DR

This paper explores the effects of torsion in a five-dimensional non-Riemannian bulk on a four-dimensional brane, extending Einstein's equations and deriving cosmological implications such as a 5D cosmological constant.

Contribution

It extends the Israel-Darmois matching conditions to include torsion in a non-Riemannian bulk and models a flat FLRW universe with a torsion-induced 5D cosmological constant.

Findings

Torsion discontinuities relate to matter distribution.

Extended Einstein equations incorporate bulk torsion effects.

A model with a torsion-induced 5D cosmological constant is developed.

Abstract

We carefully investigate the modified Einstein's field equation in a four dimensional (3-brane) arbitrary manifold embedded in a five dimensional Non-Riemannian bulk spacetime with a noncompact extra dimension. In this context the Israel-Darmois matching conditions are extended assuming that the torsion in the bulk is continuous. The discontinuity in the torsion first derivatives are related to the matter distribution through the field equation. In addition, we develop a model that describes a flat FLRW model embedded in a 5-dimensional de Sitter or Anti de Sitter, where a 5-dimensional cosmological constant emerges from the torsion.