On Weyl cosmology in five dimensions and the cosmological constant

TL;DR

This paper explores how a cosmological constant can be geometrically induced from a five-dimensional Weyl integrable space, linking higher-dimensional geometry to four-dimensional cosmological observations.

Contribution

It demonstrates that the cosmological constant can be derived from extra-dimensional Weyl geometry within the induced matter framework.

Findings

The cosmological constant arises from the Weyl scalar field in five dimensions.

Four-dimensional Einstein equations include an induced energy-momentum tensor and a cosmological constant.

The approach connects higher-dimensional Weyl geometry to observable cosmological effects.

Abstract

In this talk notes we expose the possibility to induce the cosmological constant from extra dimensions, in a geometrical framework where our four-dimensional Riemannian space-time is embedded into a five-dimensional Weyl integrable space. In particular following the approach of the induced matter theory, we show that when go down from five to four dimensions, we may recover in the context of the general theory of relativity, the induced energy momentum tensor of the induced matter theory plus a cosmological constant term, that is determined by the presence of the Weyl scalar field on the bulk.