The Logotropic Dark Fluid: Observational and Thermodynamic Constraints

We have considered a spatially flat, homogeneous and isotropic FLRW Universe filled with a single fluid, known as logotropic dark fluid (LDF), whose pressure evolves through a logarithmic equation of state. We use the recent Pantheon SNIa and cosmic chronometer datasets to constrain the parameters of this model, the present fraction of dark matter $\Omega_{m0}$ and the Hubble constant $H_0$. We find that the mean values of these parameters are $\Omega_{m0}=0.288\pm 0.012$ and $H_{0}=69.652\pm 1.698~{\rm km/s/Mpc}$ at the $1\sigma$ CL. We also find that the LDF model shows a smooth transition from the deceleration phase to acceleration phase of the universe in the recent past. We notice that the redshift of this transition $z_{t}=0.706\pm 0.048$ ($1\sigma$ error) and is well consistent with the present observations. Interestingly, we find that the Universe will settle down to a $\Lambda$CDM model in future and there will not be any future singularity in the LDF model. Furthermore, we notice that there is no significant difference between the LDF and $\Lambda$CDM models at the present epoch, but the difference (at the percent level) between these models is found as the redshift increases. We have also studied the generalized second law of thermodynamics at the dynamical apparent horizon for the LDF model with the Bekenstein and Viaggiu entropies.