Integrability and cosmological solutions in Einstein-Æther-Weyl theory

We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-AE ther theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann-Lemaitre-Robertson-Walker background space. We show that the theory admits cosmological solutions of special interests. In addition, we prove that the cosmological field equations admit the Lewis invariant as a second conservation law, which indicates the integrability of the field equations.

Automated summary

This research investigates a Lorentz violating scalar field cosmological model based on the modified Einstein-AE ther theory defined in Weyl integrable geometry. It explores the existence of exact and analytic solutions in the case of a spatially flat Friedmann-Lemaitre-Robertson-Walker background space, showing that the theory has cosmological solutions of special interests. Additionally, it demonstrates that the cosmological field equations have the Lewis invariant as a second conservation law, indicating the integrability of the field equations.