Generalized Logotropic Models and Their Cosmological Constraints
Résumé
We propose a new class of cosmological unified dark sector models called “Generalized Logotropic Models”. They depend on a free parameter n. The original logotropic model is a special case of our generalized model corresponding to . The CDM model is recovered for . In our scenario, the Universe is filled with a single fluid, a generalized logotropic dark fluid (GLDF), whose pressure P includes higher order logarithmic terms of the rest-mass density . The total energy density is the sum of the rest-mass energy density and the internal energy density u which play the roles of dark matter energy density and dark energy density , respectively. We investigate the cosmological behavior of the generalized logotropic models by focusing on the evolution of the energy density, scale factor, equation of state parameter, deceleration parameter and squared speed of sound. Low values of are favored. We also study the asymptotic behavior of the generalized logotropic models. In particular, we show that the model presents a phantom behavior and has three distinct ways of evolution depending on the value of n. For , it leads to a little rip and for to a big rip. We predict the value of the big rip time as a function of n without any free (undetermined) parameter.
Mots clés
dark energy theory
dark matter theory
cosmology
unified dark sector
logotropic model
energy: density
dark energy: density
energy: internal
dark matter: energy
velocity: acoustic
big rip
fluid
phantom
equation of state
pressure
higher-order
mass: density
asymptotic behavior
cosmological model
deceleration