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

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.