# Extended logotropic fluids as unified dark energy models

## TL;DR

This paper explores extended logotropic fluids as unified dark energy models, deriving their thermodynamic and dynamical properties, and demonstrating their potential to explain cosmic acceleration without a cosmological constant.

## Contribution

It introduces an extended version of Anton-Schmidt cosmic fluids, analyzes their Lagrangian formulations, and connects them to generalized Chaplygin gas models, expanding the theoretical framework of dark energy models.

## Key findings

- The low-energy regime can drive cosmic acceleration without a cosmological constant.
- The non-relativistic Lagrangian of the extended model coincides with that of generalized Chaplygin gas.
- The model generalizes logotropic dark energy models with new thermodynamic and dynamical insights.

## Abstract

We here study extended classes of logotropic fluids as \textit{unified dark energy models}. Under the hypothesis of the Anton-Schmidt scenario, we consider the universe obeying a single fluid whose pressure evolves through a logarithmic equation of state. This result is in analogy with crystals under isotropic stresses. Thus, we investigate thermodynamic and dynamical consequences by integrating the speed of sound to obtain the pressure in terms of the density, leading to an extended version of the Anton-Schmidt cosmic fluids. Within this picture, we get significant outcomes expanding the Anton-Schmidt pressure in the infrared regime. The low-energy case becomes relevant for the universe to accelerate without any cosmological constant. We therefore derive the effective representation of our fluid in terms of a Lagrangian $\mathcal{L}=\mathcal{L}(X)$, depending on the kinetic term $X$ only. We analyze both the relativistic and non-relativistic limits. In the non-relativistic limit we construct both the Hamiltonian and Lagrangian in terms of density $\rho$ and scalar field $\vartheta$, whereas in the relativistic case no analytical expression for the Lagrangian can be found. Thus, we obtain the potential as a function of $\rho$, under the hypothesis of irrotational perfect fluid. We demonstrate that the model represents a natural generalization of \emph{logotropic dark energy models}. Finally, we analyze an extended class of generalized Chaplygin gas models with one extra parameter $\beta$. Interestingly, we find that the Lagrangians of this scenario and the pure logotropic one coincide in the non-relativistic regime.