Tension between SN and BAO: current status and future forecasts

Using real and synthetic Type Ia SNe (SNeIa) and baryon acoustic oscillations (BAO) data representing current observations forecasts, this paper investigates the tension between those probes in the dark energy equation of state (EoS) reconstruction considering the well known CPL model and Wang's low correlation reformulation. In particular, here we present simulations of BAO data from both the the radial and transverse directions. We also explore the influence of priors on Omega_m and Omega_b on the tension issue, by considering 1-sigma deviations in either one or both of them. Our results indicate that for some priors there is no tension between a single dataset (either SNeIa or BAO) and their combination (SNeIa+BAO). Our criterion to discern the existence of tension (sigma-distance) is also useful to establish which is the dataset with most constraining power; in this respect SNeIa and BAO data switch roles when current and future data are considered, as forecasts predict and spectacular quality improvement on BAO data. We also find that the results on the tension are blind to the way the CPL model is addressed: there is a perfect match between the original formulation and that by the low correlation optimized, but the errors on the parameters are much narrower in all cases of our exhaustive exploration, thus serving the purpose of stressing the convenience of this reparametrization.