The Logotropic Dark Fluid: Observational and Thermodynamic Constraints

We have considered a 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 latest Hubble data 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 best-fit values of these parameters are Omega_{m0}=0.253 and H_{0}=70.35 kms^{-1}Mpc^{-1}, which is approximately the mean value of the global and local measurements of H_0 at the 1sigma C.L. The best-fit values obtained from this dataset are then applied to examine the evolutionary history of the logotropic equation of state and the deceleration parameter. Our study shows that the Universe is indeed undergoing an accelerated expansion phase following the decelerated one. We also measure the redshift of this transition (i.e., the cosmological deceleration-acceleration transition) z_t=0.81 and is well consistent with the present observations. Interestingly, we find that the Universe will settle down to a LCDM model in future and there will not be any future singularity in the LDF model. Furthermore, we compare the LDF and LCDM models. We notice that there is no significant difference between the LDF and LCDM models at the present epoch, but the difference (at the percent level) between these models is found as the redshift increases. These dynamical features of the LDF can be effective in determining the late-time evolution of the Universe and thus may provide an answer to the coincidence problem. 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. Our analysis has yielded a thermodynamically allowable range for the parameter B, 0 leq B leq 0.339, thereby supporting the value, B=3.53 \times 10^{-3} obtained by Chavanis from galactic observations[16].