Exploring Cosmological Expansion Parametrizations with the Gold SnIa Dataset

Abstract

We use the SnIa Gold dataset to compare LCDM with 10 representative parametrizations of the recent Hubble expansion history $H(z)$. For the comparison we use two statistical tests; the usual $χ_{min}^2$ which is insensitive to the parametrization number of parameters, and a statistic we call the p-test which depends on both the value of $χ_{min}^2$ and the number $n$ of the parametrization parameters. The p-test measures the confidence level to which the parameter values corresponding to LCDM are excluded from the viewpoint of the parametrization tested. For example, for a linear equation of state parametrization $w(z)=w_0 + w_1 z$ the LCDM parameter values ($w_0=-1$, $w_1=0$) are excluded at 75% confidence level. We use a flat prior and $Ω_{0m}=0.3$. All parametrizations tested are consistent with the Gold dataset at their best fit. According to both statistical tests, the worst fits among the 10 parametrizations, correspond to the Chaplygin gas, the brane world and the Cardassian parametrizations. The best fit is achieved by oscillating parametrizations which can exclude the parameter values corresponding to LCDM at 85% confidence level. Even though this level of significance does not provide a statistically significant exclusion of LCDM (it is less than $2σ$) and does not by itself constitute conclusive evidence for oscillations in the cosmological expansion, when combined with similar independent recent evidence for oscillations coming from the CMB and matter power spectra it becomes an issue worth of further investigation.