Bayesian Analysis and Constraints on Kinematic Models from Union SNIa

TL;DR

This paper uses supernova data to analyze various kinematic models of the universe's expansion, estimating parameters like deceleration and jerk, and comparing these models to the standard Lambda Cold Dark Matter model.

Contribution

It introduces a Bayesian framework to constrain kinematic models of cosmic expansion using supernova data, providing analytical expressions and confidence intervals for key parameters.

Findings

All models indicate current acceleration and past deceleration.

Transition redshift around 0.5, compatible with Lambda CDM.

Current data cannot strongly discriminate among models.

Abstract

The kinematic expansion history of the universe is investigated by using the 307 supernovae type Ia from the Union Compilation set. Three simple model parameterizations for the deceleration parameter (constant, linear and abrupt transition) and two different models that are explicitly parametrized by the cosmic jerk parameter (constant and variable) are considered. Likelihood and Bayesian analyses are employed to find best fit parameters and compare models among themselves and with the flat $\Lambda$CDM model. Analytical expressions and estimates for the deceleration and cosmic jerk parameters today ($q_0$ and $j_0$) and for the transition redshift ($z_t$) between a past phase of cosmic deceleration to a current phase of acceleration are given. All models characterize an accelerated expansion for the universe today and largely indicate that it was decelerating in the past, having a transition redshift around 0.5. The cosmic jerk is not strongly constrained by the present supernovae data. For the most realistic kinematic models the $1\sigma$ confidence limits imply the following ranges of values: $q_0\in[-0.96,-0.46]$, $j_0\in[-3.2,-0.3]$ and $z_t\in[0.36,0.84]$, which are compatible with the $\Lambda$CDM predictions, $q_0=-0.57\pm0.04$, $j_0=-1$ and $z_t=0.71\pm0.08$. We find that even very simple kinematic models are equally good to describe the data compared to the concordance $\Lambda$CDM model, and that the current observations are not powerful enough to discriminate among all of them.