Minisuperspace Quantum Cosmology in Metric and Affine Theories of Gravity

TL;DR

This paper develops minisuperspace quantum cosmology models for extended theories of gravity, including $f(R)$, $f(T)$, and $f( ext{Gauss-Bonnet})$, using Hamiltonian formalism and Noether symmetries to derive cosmological solutions.

Contribution

It introduces a Hamiltonian formalism for extended gravity theories in minisuperspace and derives quantum cosmology models with solutions based on Noether symmetries.

Findings

Derived minisuperspace quantum models for $f(R)$, $f(T)$, and $f( ext{Gauss-Bonnet})$ gravity.

Obtained cosmological solutions using Noether symmetries.

Applied the Hartle criterion to interpret solutions as observable universes.

Abstract

Minisuperpace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from various points of view, extend Einstein's General Relativity. Specifically, the Hamiltonian formalism for $f(R)$, $f(T)$ and $f(\mathcal{G})$ gravity, with $R$, $T$, and $\mathcal{G}$ being the curvature, torsion and Gauss--Bonnet scalars, respectively, is developed starting from the Arnowitt-Deser-Misner approach. The Minisuperspace Quantum Cosmology is derived for all these models and cosmological solutions are obtained thanks to the existence of Noether symmetries. The Hartle criterion allows the interpretation of solutions in view of observable universes.