Gravitational waves from a Weyl-Integrable manifold: a new formalism

TL;DR

This paper introduces a novel formalism for gravitational waves within a Weyl-Integrable manifold framework, incorporating torsion and non-metricity, leading to new wave equations and insights into early universe cosmology.

Contribution

It develops a new variational approach on extended geometries to derive gravitational wave equations considering non-metricity and boundary conditions.

Findings

Derived two different gravitational wave equations.

Identified potential sources for the cosmological constant.

Analyzed gravitational waves in a pre-inflationary cosmological model.

Abstract

We study the variational principle over an Hilbert-Einstein like action for an extended geometry taking into account torsion and non-metricity. By extending the semi-Riemannian geometry, we obtain an effective energy-momentum tensor which can be interpreted as physical sources. As an application we develop a new manner to obtain the gravitational wave equations on a Weyl-integrable manifold taking into account the non-metricity and non-trivial boundary conditions on the minimization of the action, which can be identified as possible sources for the cosmological constant and provides two different equations for gravitational waves. We examine gravitational waves in a pre-inflationary cosmological model.