Bayesian comparison of nonstandard cosmologies using type Ia supernovae and BAO data

We use the most recent type Ia supernovae (SNe Ia) observations to perform a statistical comparison between the standard $Λ$CDM model and its extensions [$w$CDM and $w(z)$CDM] and some alternative cosmologies: namely, the Dvali--Gabadadze--Porrati (DGP) model, a power-law $f(R)$ scenario in the metric formalism and an example of vacuum decay [$Λ(t)$CDM] cosmology in which the dilution of pressureless matter is attenuated with respect to the usual $a^{-3}$ scaling due to the interaction of the dark matter and dark energy fields. We perform a Bayesian model selection analysis using the \textsc{MultiNest} algorithm. To obtain the posterior distribution for the parameters of each model, we use the joint light-curve analysis (JLA) SNe Ia compilation containing 740 events in the interval $0.01 < z < 1.3$ along with current measurements of baryon acoustic oscillations (BAO). The JLA data are analyzed with the SALT2 light-curve fitter and the model selection is then performed by computing the Bayesian evidence of each model and the Bayes factor of the $Λ$CDM cosmology related to the other models. The results indicate that the JLA data alone are unable to distinguish the standard $Λ$CDM model from some of its alternatives but its combination with current measurements of baryon acoustic oscillations shows up an ability to distinguish them. In particular, the DGP model is practically not supported by both the BAO and the joint JLA + BAO data sets compared to the standard scenario. Finally, we provide a rank order for the models considered.