On the Hojman conservation quantities in FRW Cosmology

TL;DR

This paper explores the application of Hojman symmetry to identify conserved quantities in various cosmological models, including scalar-tensor theories and higher-order dynamical systems, providing new integrals of motion.

Contribution

It introduces the use of Hojman symmetry to find conserved quantities in FRW cosmology and extends the formalism to higher-order equations of motion.

Findings

Derived conserved quantities for specific cosmological models

Obtained exact integrals of motion in scalar-tensor cosmology

Extended Hojman symmetry formalism to higher-order systems

Abstract

In the present work we investigate the Hojman symmetry in FRW cosmology. In particular, we use the Hojman symmetry to find conserved quantities of particular cosmological models. Next, we study the Hojman symmetry in the scalar-tensor cosmology and find corresponding exact forms of integrals of motion. Finally, the formalism of the Hojman symmetry is extended to dynamical systems with the higher-order equations of motion.