Exploring Models of Running Vacuum Energy with Viscous Dark Matter from a Dynamical System Perspective

TL;DR

This paper combines running vacuum energy models with viscous dark matter in a dynamical system framework to explore their combined cosmological effects, revealing new stable solutions and deviations from the standard ΛCDM model.

Contribution

It introduces a combined model of running vacuum and viscous dark matter analyzed through dynamical systems, uncovering new phase space structures and stability conditions.

Findings

Identification of four distinct classes of models.

Critical points with non-trivial stability properties.

Numerical solutions showing deviations from ΛCDM for certain parameters.

Abstract

Running vacuum models and viscous dark matter scenarios beyond perfect fluid idealization are two appealing theoretical strategies that have been separately studied as alternatives to solve some problems rooted in the $\Lambda$CDM cosmological model. In this paper, we combine these two notions in a single cosmological setting and investigate their cosmological implications, paying particular attention in the interplay between these two constituents in different cosmological periods. Specifically, we consider a well-studied running vacuum model inspired by renormalization group, and a recently proposed general parameterization for the bulk viscosity $\xi$. By employing dynamical system analysis, we explore the physical aspects of the new phase space that emerges from the combined models and derive stability conditions that ensure complete cosmological dynamics. We identify four distinct classes of models and find that the critical points of the phase space are non-trivially renewed compared to the single scenarios. We then proceed, in a joint and complementary way to the dynamical system analysis, with a detailed numerical exploration to quantify the impact of both the running parameter and the bulk viscosity coefficient on the cosmological evolution. Thus, for some values of the model parameters, numerical solutions show qualitative differences from the $\Lambda$CDM model, which is phenomenologically appealing in light of cosmological observations.