Cosmological General Relativity With Scale Factor and Dark Energy

TL;DR

This paper develops a cosmological model based on four-dimensional space-velocity general relativity, incorporating dark energy and evolving parameters, and compares it with high-redshift supernova data.

Contribution

It derives a general solution to Einstein's equations in this framework, including dark energy effects and the Carmeli model as a special case.

Findings

Model fits high-redshift supernova data

Includes evolving dark energy in cosmological equations

Derives redshift-distance relations for cosmological analysis

Abstract

In this paper the four-dimensional space-velocity Cosmological General Relativity of Carmeli is developed by a general solution to the Einstein field equations. The metric is given in the Tolman form and the vacuum mass density is included in the energy-momentum tensor. The scale factor redshift equation is obtained, forming the basis for deriving the various redshift-distance relations of cosmological analysis. A linear equation of state dependent on the scale factor is assumed to account for the effects of an evolving dark energy in the expansion of the universe. Modeling simulations are provided for a few combinations of mass density, vacuum density and state parameter values over a sample of high redshift SNe Ia data. Also, the Carmeli cosmological model is derived as a special case of the general solution.