Comparison of cosmological models using recent supernova data

We study the expansion history of the universe up to a redshift of $\mathrm{z}=1.75\mathrm{}$ 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 $H\left(z\right)\mathrm{}$ ansatze, determine the best fit values of their parameters and rank them according to increasing value of ${\chi }_{\min }^2$ [the minimum value of ${\chi }^2$ for each $H\left(z\right)\mathrm{}$ ansatz]. We treat ${\Omega }_{0m}$ as a parameter using a reasonable prior and assume flat geometry of the universe. No prior assumptions are made about validity of energy conditions. The fitted models are fourteen and include standard cold dark matter (SCDM), cold dark matter with cosmological constant Λ (LCDM), dark energy with constant equation of state parameter w (quiessence), third order polynomial for $H(1+z),$ Chaplygin gas, Cardassian model, ${w\left(z\right)=w}_0{+w}_{1}z,$ ${w\left(z\right)=w}_0{+zw}_1/(1+z),$ an oscillating ansatz for $H\left(z\right),$ 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 $w\left(z\right)\mathrm{}$ and $H\left(z\right)\mathrm{}$ at best fit. The worst fit among the data-consistent models considered corresponds to the simplest model LCDM $({\chi }_{\min }^2=198.7\mathrm{}$ for ${\Omega }_{0m}=0.34)$ while the best fit is achieved by the three parameter oscillating ansatz $({\chi }_{\min }^2=193.8).\mathrm{}$ Most of the best fit ansatze have an equation of state parameter $w\left(z\right)\mathrm{}$ that varies between $w\left(z\right)\mathrm{}\simeq -1$ for $z<\mathrm{}0.5\mathrm{}$ to $w\left(z\right)>0\mathrm{}$ for $z>\mathrm{}1.\mathrm{}$ 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 $H\left(z\right)\mathrm{}$ ansatz lends further support to this possibility.