Time-dependent extra dimension and higher-dimensional modifications to the matter content in FRW spacetimes

TL;DR

This paper explores how different methods of slicing a 5D manifold influence the induced matter content in 4D FRW spacetimes, highlighting the role of time-dependent and static foliations in higher-dimensional cosmology.

Contribution

It introduces a new approach using static foliations for deriving 4D matter content from 5D manifolds, expanding beyond previous moving hypersurface methods.

Findings

Different foliation methods lead to distinct matter content in 4D.

Static foliation approach offers alternative insights into higher-dimensional modifications.

Results depend critically on how the 4D universe is embedded in the 5D manifold.

Abstract

In this work we suggest that higher-dimensional modifications to the matter content in FRW spacetimes can be obtained not only, as first considered by Ponce de Leon, referring to "moving" 4D hypersurfaces non-orthogonal to the time-dependent extra dimension of an embedding 5D manifold, but also referring to "fixed" 4D hypersurfaces orthogonal to a suitable scalar function which defines a static foliation of the 5D manifold and takes the role of the extra dimension in a suitable coordinate system. Results obtained in each approach crucially depend on the method used to identify the 4D metric of our brane universe from the 5D metric of the bulk manifold.