Bayesian evidence and model selection approach for time-dependent dark energy

We use parameterized post-Friedmann (PPF) description for dark energy and apply ellipsoidal nested sampling to perform the Bayesian model selection method on different time-dependent dark energy models using a combination of $Planck$ and data based on distance measurements, namely baryon acoustic oscillations and supernovae luminosity distance. Models with two and three free parameters described in terms of linear scale factor $a$, or scaled in units of e-folding $\ln a$ are considered. Our results show that parameterizing dark energy in terms of $\ln a$ provides better constraints on the free parameters than polynomial expressions. In general, two free-parameter models are adequate to describe the dynamics of the dark energy compared to their three free-parameter generalizations. According to the Bayesian evidence, determining the strength of support for cosmological constant $\Lambda$ over polynomial dark energy models remains inconclusive. Furthermore, considering the $R$ statistic as the tension metric shows that one of the polynomial models gives rise to a tension between $Planck$ and distance measurements data sets. The preference for the logarithmic equation of state over $\Lambda$ is inconclusive, and the strength of support for $\rm \Lambda$CDM over the oscillating model is moderate.