Canonical Structure and Hidden Symmetries in Scalar Field Cosmology

TL;DR

This paper uncovers hidden symmetries in scalar field cosmology, revealing canonical transformations that simplify equations and connect different cosmological models, including interacting fields and $ ext{Lambda}$-cosmology.

Contribution

It introduces a set of canonical transformations for scalar field cosmology with exponential potentials, enabling simplified equations and mappings between various cosmological models.

Findings

Existence of canonical transformations for exponential potentials.

Mapping solutions with interaction terms to simpler free particle models.

Relation between scalar field and $ ext{Lambda}$-cosmology solution spaces.

Abstract

We investigate hidden symmetries in minimally coupled scalar field cosmology within the FLRW universe, and a perfect fluid with and without interaction to the scalar field. We show that for an exponential potential there exists a set of canonical transformations through which the cosmological field equations can be recast in the form of a free particle in flat space. Based on this equivalence, we construct a mapping that generates cosmological solutions with interaction terms, corresponding to a chameleon mechanism. Finally, we discuss how this class of canonical transformations can relate the solution spaces of different cosmological models, such as of the scalar field and of the $\Lambda$-Cosmology.