Weighing Cosmological Models with SNe Ia and Gamma Ray Burst Redshift Data

Abstract

Many models have been proposed to explain the intergalactic redshift using different observational data and different criteria for the goodness-of-fit of a model to the data. The purpose of this paper is to examine several suggested models using the same supernovae Ia data and gamma-ray burst (GRB) data with the same goodness-of-fit criterion and weigh them against the standard Lambda cold dark matter model (ΛCDM). We have used the redshift—distance modulus (z − μ) data for 580 supernovae Ia with 0.015 ≤ z ≤ 1.414 to determine the parameters for each model and then use these model parameter to see how each model fits the sole SNe Ia data at z = 1.914 and the GRB data up to z = 8.1. For the goodness-of-fit criterion, we have used the chi-square probability determined from the weighted least square sum through non-linear regression fit to the data relative to the values predicted by each model. We find that the standard ΛCDM model gives the highest chi-square probability in all cases albeit with a rather small margin over the next best model—the recently introduced nonadiabatic Einstein de Sitter model. We have made (z − μ) projections up to z = 1096 for the best four models. The best two models differ in μ only by 0.328 at z = 1096, a tiny fraction of the measurement errors that are in the high redshift datasets.