Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology

TL;DR

This paper explores Hamiltonian dynamics and Noether symmetries in extended gravity cosmologies, demonstrating how conserved quantities help classify cosmic behaviors and singularities across various models.

Contribution

It introduces a general framework for identifying Noether symmetries in extended gravity cosmologies and shows their role in classical behavior selection and singularity classification.

Findings

Noether symmetries exist in various extended gravity models.

Conserved quantities guide the selection of classical cosmic evolution.

Symmetry breaking points correspond to cosmological singularities.

Abstract

We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives selection rule to recover classical behaviors in cosmic evolution according to the so called Hartle criterion, that allows to select correlated regions in the configuration space of dynamical variables. We show that such a statement works for general classes of Extended Theories of Gravity and is conformally preserved. Furthermore, the presence of Noether symmetries allows a straightforward classification of singularities that represent the points where the symmetry is broken. Examples of nonminimally coupled and higher-order models are discussed.