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.