Non-linear causal bulk viscosity in Unified Dark Matter Cosmologies

We propose a bulk viscous unified dark matter scenario based on a nonlinear 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, ξ= ξ₀ ρₘˢ, treating s as a free parameter, 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 ξ₀ 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 ≥ 1/2. In contrast to the generic s ≠ 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 ξ₀, relaxing the strong bounds ξ₀ ~ O(1) required in Eckart-based viscous models.