Late-time evolution of cosmological models with fluids obeying a Shan-Chen-like equation of state

TL;DR

This paper investigates the late-time behavior of cosmological models with fluids obeying a Shan-Chen-like equation of state, analyzing classical equilibrium solutions and quantum effects to understand their evolution without future singularities.

Contribution

It provides a combined classical and quantum analysis of Shan-Chen-like fluids in cosmology, revealing stable equilibrium solutions and the absence of future singularities.

Findings

Existence of two classical equilibrium solutions depending on parameters

No development of future cosmological singularities in the model

Quantum analysis supports classical stability and smooth evolution

Abstract

Classical as well as quantum features of the late-time evolution of cosmological models with fluids obeying a Shan-Chen-like equation of state are studied. The latter is of the type $p=w_{\rm eff}(\rho)\,\rho$, and has been used in previous works to describe, e.g., a possible scenario for the growth of the dark-energy content of the present Universe. At the classical level the fluid dynamics in a spatially flat Friedmann-Robertson-Walker background implies the existence of two possible equilibrium solutions depending on the model parameters, associated with (asymptotic) finite pressure and energy density. We show that no future cosmological singularity is developed during the evolution for this specific model. The corresponding quantum effects in the late-time behavior of the system are also investigated within the framework of quantum geometrodynamics, i.e., by solving the (minisuperspace) Wheeler-DeWitt equation in the Born-Oppenheimer approximation, constructing wave-packets and analyzing their behavior.