Geometry and Matter Reduction in a 5D Kaluza-Klein Framework

TL;DR

This paper develops a consistent 5D Kaluza-Klein framework incorporating matter, removing massive mode issues without relaxing compactification, and derives 4D effective equations including additional scalar fields for cosmological applications.

Contribution

It introduces a new approach to matter in 5D Kaluza-Klein theory that avoids massive mode problems and derives comprehensive 4D equations with extra scalar fields.

Findings

Removal of massive mode issues without relaxing compactification

Derivation of 4D equations with additional scalar fields

Discussion of cosmological scenarios involving these scalar fields

Abstract

In this paper we consider the Kaluza-Klein fields equations in presence of a generic 5D matter tensor which is governed by a conservation equation due to 5D Bianchi identities. Following a previous work, we provide a consistent approach to matter where the problem of huge massive modes is removed, without relaxing the compactification hypotheses; therefore we perform the dimensional reduction either for metric fields and for matter, thus identifying a pure 4D tensor term, a 4D vector term and a scalar one. Hence we are able to write down a consistent set of equations for the complete dynamics of matter and fields ; with respect to the pure Einstein-Maxwell system we now have two additional scalar field: the usual dilaton one plus a scalar source term. Some significant scenarios involving these terms are discussed and perspectives for cosmological applications are suggested.