Generalized Logotropic Models and their Cosmological Constraints*

We propose a new class of cosmological unified dark sector models called "{\em Generalized Logotropic Models}". The logotropic model is just a special case of our generalized model. 

In our scenario, the Universe is filled with a single fluid, known as generalized logotropic dark fluid (GLDF), whose pressure $P$ includes all higher order logarithmic terms of the rest mass density $\rho$. As a consequence, the total energy density $\epsilon$ is the sum of the dark matter density $\epsilon_m$ and the dark energy density $\epsilon_{de}$. From the best fits values of the present fraction of dark matter $\Omega_{m,0}$ and  $B$ obtained from the usual logotropic mode, we have investigated the cosmological behavior of the generalized logotropic models by focusing on the evolution of the dark energy density, scale factor, equation of state, acceleration and squared speed of sound parameters. Lower values of $n$ are more favored. We have also studied the asymptotic behavior of the generalized logotropic models. In particular, we have shown that the model has three distinct ways of evolution depending on the value of $n$.