Variational symmetries and superintegrability in multifield cosmology

TL;DR

This paper classifies scalar field potentials in multifield cosmology that admit variational symmetries, derives conservation laws, finds analytic solutions, and analyzes their stability, providing insights into inflationary models.

Contribution

It introduces a classification of potentials with variational symmetries in multifield cosmology and derives exact solutions and stability analysis.

Findings

Identified potentials with variational symmetries leading to conservation laws.

Obtained analytic solutions for specific potential forms.

Analyzed stability of scaling solutions in inflationary scenarios.

Abstract

We consider a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker background space with an ideal gas and a multifield Lagrangian consisting of two minimally coupled scalar fields which evolve in a field space of constant curvature. For this cosmological model we classify the potential function for the scalar fields such that variational point symmetries exist. The corresponding conservation laws are calculated. Finally, analytic solutions are presented for specific functional forms of the scalar field potential in which the cosmological field equations are characterized as a Liouville integrable system by point symmetries. The free parameters of the cosmological model are constrained in order to describe analytic solutions for an inflationary epoch. Finally, stability properties of exact closed-form solutions are investigated. These solutions are scaling solutions with important physical properties for the cosmological model.