Elliptical Solutions to the Standard Cosmology Model with Realistic Values of Matter Density

TL;DR

This paper explores elliptical solutions to the standard cosmological model with realistic matter density values, revealing critical points at certain redshifts and implications for the evolution of the cosmological constant.

Contribution

It introduces elliptical solutions to the FRW model with wide parameter ranges, highlighting potential critical points and the evolving dominance of the cosmological constant.

Findings

Critical points at redshift z between 1 and 3 for positive Omega_L

Omega_L may increase in dominance over cosmic evolution

Positive Omega_L tends to be attractive at high redshifts

Abstract

We have examined a solution to the FRW model of the Einstein and de Sitter Universe, often termed the standard model of cosmology, using wide values for the normalized cosmological constant Omega_L and spacetime curvature Omega_k with proposed values of normalized matter density. These solutions were evaluated using a combination of the third type of elliptical equations and were found to display critical points for redshift z, between 1 and 3, when Omega_L is positive. These critical points occur at values for normalized cosmological constant higher than those currently thought important, though we find this solution interesting because the Omega_L term may increase in dominance as the Universe evolves bringing this discontinuity into importance. We also find positive Omega_L tends towards attractive at values of z which are commonly observed for distant galaxies.