We have considered a spatially flat , homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker ( 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 parameter H ( z ) dataset to constrain the parameters of this model , the present fraction of dark matter \Omega _ { m 0 } and the Hubble constant H _ { 0 } .
We find that the best-fit values of these parameters are \Omega _ { m 0 } = 0.253 ^ { +0.031 } _ { -0.027 } ( 1 \sigma ) and H _ { 0 } = 70.35 ^ { +2.49 } _ { -2.50 } ~ { } ( 1 \sigma ) ~ { } { km~ { } s ^ { -1 } ~ { } Mpc ^ { -1 } } , which is approximately the mean value of the global and local measurements of H _ { 0 } at the 1 \sigma confidence level .
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 \pm 0.04 ( 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 compare the LDF and \Lambda CDM models .
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 .
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 dimensionless logotropic temperature B , 0 \leq B \leq 0.339 , thereby supporting the value , B = 3.53 \times 10 ^ { -3 } obtained by P.H .
Chavanis from galactic observations ( ( 16 ) ) .