Integrability and Cosmological Solutions in Einstein-aether-Weyl theory

TL;DR

This paper explores exact solutions and integrability in a Lorentz-violating scalar field cosmological model within Einstein-aether-Weyl theory, revealing special cosmological solutions and conserved quantities.

Contribution

It demonstrates the existence of exact solutions and proves the integrability of the field equations via the Lewis invariant in Einstein-aether-Weyl cosmology.

Findings

Existence of exact and analytic solutions for flat FLRW spacetime.

Identification of the Lewis invariant as a second conserved quantity.

Proof of integrability of the cosmological field equations.

Abstract

We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-aether theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann--Lema\^{\i}tre--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.