Analytic solutions for the $\Lambda$-FRW Model

TL;DR

This paper derives exact analytic solutions for various configurations of the $ m extit{Lambda}$-FRW cosmological model, enhancing understanding of universe dynamics with different matter, radiation, curvature, and cosmological constant parameters.

Contribution

It provides comprehensive analytic solutions for all combinations of $ m extit{Lambda}$, curvature, radiation, and matter, including the detailed $ m extit{Lambda}$CDM model.

Findings

Solutions clearly illustrate the recent onset of cosmic acceleration.

Includes models with and without radiation and matter.

Offers a complete set of formulas for different cosmological scenarios.

Abstract

The high precision attained by cosmological data in the last few years has increased the interest in exact solutions. Analytic expressions for solutions in the Standard Model are presented here for all combinations of $\Lambda = 0$, $\Lambda \ne 0$, $\kappa = 0$ and $\kappa \ne 0$, in the presence and absence of radiation and nonrelativistic matter. The most complete case (here called the $\Lambda \gamma CDM$ Model) has $\Lambda \ne 0, \kappa \ne 0$, and supposes the presence of radiation and dust. It exhibits clearly the recent onset of acceleration. The treatment includes particular models of interest such as the $\Lambda$CDM Model (which includes the cosmological constant plus cold dark matter as source constituents).