New exact solutions of Bianchi I, Bianchi III and Kantowski-Sachs spacetimes in scalar-coupled gravity theories via Noether gauge symmetries

TL;DR

This paper employs Noether gauge symmetries to find exact solutions in scalar-coupled gravity theories for Bianchi and Kantowski-Sachs cosmologies, enhancing previous symmetry approaches.

Contribution

It introduces a comprehensive set of Noether gauge symmetries for specific cosmological models in scalar-tensor gravity, leading to new exact solutions.

Findings

Derived full set of Noether gauge symmetries for models

Obtained new exact solutions using first integrals

Extended previous symmetry results with more general symmetries

Abstract

The Noether symmetry approach is useful tool to restrict the arbitrariness in a gravity theory when the equations of motion are underdetermined due to the high number of functions to be determined in the ansatz. We consider two scalar-coupled theories of gravity, one motivated by induced gravity, the other more standard; in Bianchi I, Bianchi III and Kantowski-Sachs cosmological models. For these models, we present a full set of Noether gauge symmetries, which are more general than those obtained by the strict Noether symmetry approach in our recent work. Some exact solutions are derived using the first integrals corresponding to the obtained Noether gauge symmetries.