Homogeneous cosmologies and the Maupertuis-Jacobi principle

TL;DR

This paper extends the geometric approach to analyze the dynamics of homogeneous cosmologies, including anisotropic and non-minimally coupled scalar fields, by relating them to geodesics on effective manifolds, simplifying their study.

Contribution

It generalizes the Maupertuis-Jacobi principle to more complex cosmological models, enabling geometric insights into their dynamics.

Findings

Geometrical analysis simplifies the study of complex cosmological models.

Homogeneous and anisotropic cosmologies can be understood through geodesics on effective manifolds.

Explicit examples demonstrate the utility of the geometric approach.

Abstract

A recent work showing that homogeneous and isotropic cosmologies involving scalar fields are equivalent to the geodesics of certain effective manifolds is generalized to the non-minimally coupled and anisotropic cases. As the Maupertuis-Jacobi principle in classical mechanics, such result permits us to infer some dynamical properties of cosmological models from the geometry of the associated effective manifolds, allowing us to go a step further in the study of cosmological dynamics. By means of some explicit examples, we show how the geometrical analysis can simplify considerably the dynamical analysis of cosmological models.