A comparison of cosmological models using recent supernova data

S. Nesseris and L. Perivolaropoulos
Department of Physics, University of Ioannina, Greece


We study the expansion history of the universe up to a redshift of z=1.75 using the 194 recently published SnIa data by Tonry et. al. and Barris et. al. In particular we find the best fit forms of several cosmological models and H(z) ansatze, determine the best fit values of their parameters and rank them according to increasing value of cmin2 (the minimum value of c2 for each H(z) ansatz). We use a prior of W0m = 0.3 and assume flat geometry of the universe. No prior assumptions are made about validity of energy conditions. The fitted models are fourteen and include SCDM, LCDM, dark energy with constant equation of state parameter w (quiessence), third order polynomial for H(1+z), Chaplygin gas, Cardassian model, w(z)=w0 + w1 z, w(z)=w0 + z w1/(1+z), an oscillating ansatz for H(z) etc. All these models with the exception of SCDM are consistent with the present data. However, the quality of the fit differs significantly among them and so do the predicted forms of w(z) and H(z) at best fit. The worst fit among the data-consistent models considered corresponds to the simplest model LCDM (cmin2 = 198.7 for W0m = 0.34) while the best fit is achieved by the three parameter oscillating ansatz (cmin2 = 194.1). Most of the best fit ansatze have a w(z) that varies between w(z) @ -1 for z < 0.5 to w(z) > 0 for z > 1. This implies that the sign of the pressure of the dark energy may be alternating as the redshift increases. The goodness of fit of the oscillating H(z) ansatz lends further support to this possibility.

The best fit effective equation of state parameter w(z) for various cosmological models
(the number in parenthesis indicates the goodness of fit χmin2 and the rank of the model 1-13 )

Numerical Analysis

The file chi2.nb has been used for the numerical analysis of the paper and is based on Mathematica 4.  It takes about 20min to run on P4 2.6GHz and it produces all the 4 figures of the paper.  The code is fairly simple and some explanatory comments are included in the file.

It can be downloaded using the link below in a zip file (less than 1Mb) along with the source files of the paper. The 194 SnIa data file is also included within the zip file. The data-file should be placed in a directory called c:\mathfiles under the name data1.txt before runing chi2.nb.

Download pdf file of paper

Download  the mathematica file for data analysis,  the 194 SnIa data file and the paper