A cosmographic analysis of the transition to acceleration using SN-Ia and BAO

We explore the distance-redshift relation using a cosmographic methodology, and show how the cosmographic parameters can be used to determine the redshift of transition from deceleration to acceleration. Such a transition at a low redshift occupies only a small region of the available parameter space, and the prior assumption of an early period of deceleration can significantly change the posterior constraints. We use available type Ia Supernovae (SN-Ia) and Baryon Acoustic Oscillation (BAO) data sets to determine the cosmographic deceleration $q_0$, jerk $j_0$, snap $s_0$ and lerk $l_0$ parameters. The parameters are consistent with the $\mathrm{\Lambda }$CDM model for a flat universe within 2-sigma. We derive constraints on the redshift of transition from deceleration to acceleration for the different expansions, and find $z_{\rm acc} > 0.14$ at 95% confidence in the most conservative case.