Eur. Phys. J. C (2025) 85: 1486
https://doi.org/10.1140/epjc/s10052-025-15213-7

Regular Article - Theoretical Physics

Non-linear causal bulk viscosity in unified dark matter cosmologies

¹ Departamento de Física, Universidad de Santiago de Chile, Avenida Víctor Jara 3493, 9170124, Santiago, Chile
² Centro Multidisciplinario de Física, Vicerrectoría de Investigación, Universidad Mayor, Camino La Pirámide 5750, 8580745, Huechuraba, Chile

^a This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 22 October 2025
Accepted: 14 December 2025
Published online: 31 December 2025

Abstract

We propose a bulk viscous unified dark matter scenario based on a non-linear extension of the full causal Israel–Stewart theory. This framework allows the viscous fluid to remain far from equilibrium – an essential feature for a physically consistent description of viscosity-driven accelerated expansion. We adopt the standard parametrization for the bulk viscosity, $\xi ={\xi }_0{\rho }_m^s$, treating s as a free parameter (in contrast to most previous works), and study the model in a spatially flat Friedmann–Robertson–Walker background. By reformulating the cosmological equations as an autonomous dynamical system, we obtain both asymptotic analytical solutions and a numerical characterization of the phase space. At early times, the viscous component can mimic a stiff fluid, while at intermediate epochs it behaves like dark matter. With a suitable choice of dynamical variables, the system admits three distinct classes of late-time attractors. Two of them are separated by a basin-boundary saddle point: (i) a generic quintessence solution for $s=1/2$, which encompasses a de Sitter-like behavior when ${\xi }_0$ satisfies a specific relation involving the nonlinear parameters; (ii) a global exact de Sitter attractor for $s<1/2$; and (iii) a phantom-like solution that emerges for $s\ge 1/2$. In contrast to the generic $s\ne 1/2$ case, the $s=1/2$ scenario exhibits a qualitatively different stability structure, allowing de Sitter and phantom attractors to coexist. All solutions respect entropy production, and cosmic acceleration emerges independently of ${\xi }_0$, relaxing the strong bounds, ${\xi }_0\sim \mathcal{O}(1)$, required in Eckart-based viscous models.