The general Friedmann equation: a mathematical point of view

TL;DR

This paper classifies solutions to the general Friedmann equation with a focus on non-zero cosmological constants, using algebraic methods to identify four distinct model types and their key relations.

Contribution

It provides a comprehensive algebraic classification of Friedmann solutions without prior parameter restrictions, highlighting four fundamental model types.

Findings

Four distinct solution types identified

Explicit formulas for key parameters provided

Relations between cosmological constant, mass, and radiation density derived

Abstract

The note presents a classification of the relevant distinct types of solutions of the general Friedmann equation without assuming a priori restrictions for the parameters occurring in this equation. The emphasis is on the case of a non-vanishing cosmological constant. The classification uses algebraic criteria. The result is: There are four distinct basic types of models. Explicit formulas for decisive terms are given. Characteristic mutual relations of cosmological constant, mass and radiation density to distinguish between the models are calculated.