Extended logotropic fluids as unified dark energy models

Abstract

We study extended classes of logotropic fluids as unified dark energy models. Under the hypothesis of the Anton–Schmidt scenario, we consider a universe obeying a single fluid model with a logarithmic equation of state. We investigate the thermodynamic and dynamical consequences of an extended version of the Anton–Schmidt cosmic fluids. Specifically, we expand the Anton–Schmidt pressure in the infrared regime. The low-energy case becomes relevant for the universe as regards acceleration without any cosmological constant. We therefore derive the effective representation of our fluid in terms of a Lagrangian depending on the kinetic term only. We analyze both the relativistic and the non-relativistic limits. In the non-relativistic limit we construct both the Hamiltonian and the Lagrangian in terms of density ρ and scalar field ϑ, whereas in the relativistic case no analytical expression for the Lagrangian can be found. Thus, we obtain the potential as a function of ρ, under the hypothesis of an irrotational perfect fluid. We demonstrate that the model represents a natural generalization of logotropic dark energy models. Finally, we analyze an extended class of generalized Chaplygin gas models with one extra parameter β. Interestingly, we find that the Lagrangians of this scenario and the pure logotropic one coincide in the non-relativistic regime.