Dynamical analysis approaches in spatially curved FRW spacetimes

TL;DR

This paper reviews two general dynamical analysis methods for spatially curved FRW cosmologies, focusing on fluids with unspecified equations of state and scalar fields with positive potentials, identifying key features and symmetries.

Contribution

It introduces new dimensionless variables and evolution parameters for agnostic analysis of curved FRW models, enabling the identification of critical points and symmetries.

Findings

Identification of invariant subsets and critical points

Analysis of symmetries in the dynamical systems

Cosmological interpretation of the features

Abstract

In this article, we summarize two agnostic approaches in the framework of spatially curved Friedmann-Robertson-Walker (FRW) cosmologies discussed in detail in (Kerachian et al., 2020, 2019). The first case concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS), for which the only assumption made is the non-negativity of the fluid's energy density. The second case concerns the dynamics of a non-minimally coupled real scalar field with unspecified positive potential. For each of these models, we define a new set of dimensionless variables and a new evolution parameter. In the framework of these agnostic setups, we are able to identify several general features, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation.