Dilaton-scalar models in context of generalized affine gravity theories: their properties and integrability

TL;DR

This paper explores dilaton-scalar gravity models derived from affine generalized gravity theories, highlighting their symmetries, integrability, and potential for solving cosmological equations.

Contribution

It introduces a new class of dilaton-scalar models from fundamental gravity modifications and analyzes their symmetries and integrability properties.

Findings

Models possess symmetries similar to GR with scalar fields

Constructed additional first integrals for the models

Formulated an integral equation suitable for iterative solutions

Abstract

Nowadays it is widely accepted that the evolution of the universe was driven by some scalar degrees of freedom both on its early stage and at present. The corresponding cosmological models often involve some scalar fields introduced ad hoc. In this paper we cultivate a different approach, which is based on a derivation of new scalar degrees of freedom from fundamental modifications of Einstein's gravity. In elaboration of our previous work, we here investigate properties of the dilaton-scalar gravity obtained by dimensional reductions of a recently proposed affine generalized gravity theory. We show that these models possess the same symmetries as related models of GR with ordinary scalar fields. As a result, for a rather general class of dilaton-scalar gravity models we construct additional first integrals and formulate an integral equation well suited for solving by iterations.