Qualitative study of perfect-fluid Friedmann-Lema\^{\i}tre-Robertson-Walker models with a cosmological constant

TL;DR

This paper uses qualitative analysis to explore the dynamics of homogeneous, isotropic cosmological models with perfect fluids and a cosmological constant, highlighting their behaviors without solving complex equations.

Contribution

It introduces a qualitative, mechanics-inspired approach to analyze various cosmological models with different parameters, broadening understanding without explicit solutions.

Findings

Identifies different evolutionary behaviors depending on parameters w and mbda

Provides a framework for classifying cosmological models qualitatively

Facilitates elementary teaching of cosmological dynamics

Abstract

The evolution of spatially homogeneous and isotropic cosmological models containing a perfect fluid with equation of state p=w\rho\ and a cosmological constant \Lambda\ is investigated for arbitrary combinations of w and \Lambda, using standard qualitative analysis borrowed from classical mechanics. This approach allows one to consider a large variety of situations, appreciating similarities and differences between models, without solving the Friedmann equation, and is suitable for an elementary course in cosmology.