Exact cosmological solutions from Hojman conservation quantities

TL;DR

This paper introduces a novel method using Hojman conserved quantities to derive exact solutions in cosmological models, especially scalar-tensor theories, without relying on traditional Lagrangian or Hamiltonian frameworks.

Contribution

It develops a new approach to find exact cosmological solutions via symmetry transformations and Hojman conserved quantities, applicable to a broad class of scalar-tensor models.

Findings

Hojman conserved quantities exist for many quintessence potentials.

Exact solutions for scale factor and scalar field are obtained.

Phase-space analysis reveals general cosmological behaviors.

Abstract

We present a new approach to find exact solutions for cosmological models. By requiring the existence of a symmetry transformation vector for the equations of motion of the given cosmological model (without using either Lagrangian or Hamiltonian), one can find corresponding Hojman conserved quantities. With the help of these conserved quantities, the analysis of the cosmological model can be simplified. In the case of quintessence scalar-tensor models, we show that the Hojman conserved quantities exist for a wide range of V(\phi)-potentials and allow to find exact solutions for the cosmic scale factor and the scalar field. Finally, we investigate the general cosmological behavior of solutions by adopting a phase-space view.