Inducing the cosmological constant from five-dimensional Weyl space

TL;DR

This paper explores how a five-dimensional Weyl integrable space can induce a cosmological constant or a time-dependent parameter in four-dimensional space-time, offering a novel geometric origin for dark energy.

Contribution

It demonstrates that the Weyl field in five dimensions can generate a cosmological constant or dynamic dark energy in four dimensions, extending induced matter theory.

Findings

Weyl field contributes to the induced energy-momentum tensor.

The model can produce a time-dependent cosmological parameter.

A simple cosmological model with interesting properties is constructed.

Abstract

We investigate the possibility of inducing the cosmological constant from extra dimensions by embedding our four-dimensional Riemannian space-time into a five-dimensional Weyl integrable space. Following approach of the induced matter theory we show that when we go down from five to four dimensions, the Weyl field may contribute both to the induced energy-tensor as well as to the cosmological constant, or more generally, it may generate a time-dependent cosmological parameter. As an application, we construct a simple cosmological model which has some interesting properties.