Minisuperspace Cosmology in Extended Geometric Trinity of Gravity

TL;DR

This paper explores classical and quantum cosmology within the Extended Geometric Trinity of Gravity, using Noether symmetries to identify viable models and deriving exact solutions across different formulations of gravity.

Contribution

It demonstrates how to restore equivalence among various gravity formulations by including divergence terms and provides explicit cosmological solutions.

Findings

Equivalence among gravity formulations can be restored with divergence terms.

Exact cosmological solutions are derived for different models.

Noether symmetries help select viable gravity models.

Abstract

We investigate Extended Geometric Trinity of Gravity at both classical and quantum cosmological levels using the minisuperspace approach. Adopting Noether symmetries to select viable models, we examine metric-affine theories of gravity, in particular the extensions of General Relativity, Teleparallel Equivalent General Relativity and Symmetric Teleparallel Equivalent General Relativity, and show that the equivalence among these different formulations can be restored by including in the Lagrangian the divergence terms that relate their respective geometric invariants to the Ricci scalar. Exact cosmological solutions are derived and compared in the different models.