Study of a Viscous ΛWDM Model: Near-Equilibrium Condition, Entropy Production, and Cosmological Constraints

Abstract

Extensions to a ΛDM model have been explored in order to face current tensions that occur within its framework, which encompasses broadening the nature of the dark matter (DM) component to include warmness and a non-perfect fluid description. In this paper, we investigated the late-time cosmological evolution of an exact solution recently found in the literature, which describes a viscous warm ΛDM model (ΛWDM) with a DM component that obeys a polytropic equation of state (EoS), which experiences dissipative effects with a bulk viscosity proportional to its energy density, with proportionality constant ξ0. This solution has the particularity of having a very similar behavior to the ΛCDM model for small values of ξ0, evolving also to a de Sitter type expansion in the very far future. We explore firstly the thermodynamic consistences of this solution in the framework of Eckart’s theory of non-perfect fluids, focusing on the fulfillment of the two following conditions: (i) the near-equilibrium condition and (ii) the positiveness of the entropy production. We explore the range of parameters of the model that allow to fulfill these two conditions at the same time, finding that a viscous WDM component is compatible with both ones, being in this sense, a viable model from the thermodynamic point of view. Furthermore, we constrained the free parameters of the model with the observational data coming from supernovae Ia (SNe Ia) and the observational Hubble parameter data (OHD), using these thermodynamics analyses to define the best priors for the cosmological parameters related to the warmness and the dissipation of the DM, showing that this viscous ΛWDM model can describe the combined SNe Ia+OHD data in the same way as the ΛCDM model. The cosmological constraint at 3σ CL gives us an upper limit on the bulk viscous constant of order ξ0∼106 Pa·s, which is in agreement with some previous investigations. Our results support that the inclusion of a dissipative WDM, as an extension of the standard cosmological model, leads to a both thermodynamically consistent and properly fitted cosmological evolution.