Bayesian analysis and constraints on kinematic models from union SNIa

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 theflat ΛCDM model.Analytical expressions and estimates for the deceleration and cosmic jerk parameters today (q0 and j0) and for the transition redshift (zt) between a past phase of cosmic deceleration to a current phase of acceleration are given.All models characterize an accelerated expansion for theuniverse today and largely indicate that it was decelerating inthe 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 1σ confidence limitsimply the following ranges of values: q0 ∊ [−0.96, −0.46], j0 ∊ [−3.2, −0.3] and zt ∊ [0.36, 0.84],which are compatible with the ΛCDM predictions, q0 = −0.57 ± 0.04, j0 = −1 and zt = 0.71 ± 0.08.We find that even very simple kinematic models are equally good to describe the data compared to the concordance ΛCDM model, and that the current observations are not powerful enough to discriminate among all of them.