Modified CPL models for dark energy and observational constraints

In this work, we consider two modified Chevallier–Polarski–Linder (CPL) models in the background of homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) space–time, namely, (i) the generalized CPL model (Model I) and (ii) the logarithmic form of the equation of state for the dark energy. From the observational data sets $((\text{Pantheon}+)+\text{BAO}+\text{HST})$, we find that at the present epoch (redshift $z=0$), the equation of state for the dark energy converges almost at the same value ${\omega }_{\mathrm{\text{fld}}}\approx -0.86$ and the variation of ${\omega }_{\mathrm{\text{fld}}}(z)$ with respect to the redshift parameter is very small for both models. We also find that the present value of the Hubble parameter $H_0$ is almost same for both the models. Finally, we compare the models in the light of Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian evidence. However, we find that Model II is better compared to Model I from the estimated value of the deceleration parameter.