# Generalized Logarithmic Equation of State in Classical and Loop Quantum Cosmology Dark Energy-Dark Matter Coupled Systems

## TL;DR

This paper investigates the phase space of coupled dark energy-dark matter systems with a generalized logarithmic dark energy equation of state, revealing stable de Sitter attractors in classical and loop quantum cosmology, with broader stability conditions in the latter.

## Contribution

It introduces a generalized logarithmic dark energy equation of state and analyzes its impact on cosmological dynamics in classical and loop quantum cosmology, highlighting the existence of stable de Sitter attractors.

## Key findings

- Stable de Sitter attractors exist in both classical and loop quantum cosmology.
- Loop quantum cosmology allows a wider parameter range for stable attractors.
- Generalized logarithmic dark energy enables de Sitter solutions absent in simpler models.

## Abstract

In this paper we shall study the phase space of a coupled dark energy-dark matter fluids system, in which the dark energy has a generalized logarithmic corrected equation of state. Particularly, the equation of state for the dark energy will contain a logarithmic function of the dark energy density $\rho_d$ and will also have quadratic and Chaplygin gas-like terms, expressed in terms of $\rho_d$. We shall use the dynamical system approach in order to study the cosmological dynamics, and by appropriately choosing the dynamical system variables, we shall construct an autonomous dynamical system. The study will be performed in the context of classical and loop quantum cosmology, and the focus is on finding stable de Sitter attractors. As we demonstrate, in both the classical and loop quantum cosmology cases, there exist stable de Sitter attractors in the phase space, with the loop quantum cosmology case though having a wider range of the free parameter values for which the stable de Sitter attractors may occur. It is emphasized that the use of a generalized dark energy equation of state makes possible the existence of de Sitter attractors, which were absent in the case that a simple logarithmic term constitutes the dark energy equation of state.