Stability analysis and constraints on interacting viscous cosmology

Abstract: In this work we study the evolution of a spatially flat Universe by considering a viscous dark matter and perfect fluids for dark energy and radiation, including an interaction term between dark matter and dark energy. In the first part, we analyse the general properties of the Universe by performing a stability analysis and then we constrain the free parameters of the model using the latest and cosmological-independent measurements of the Hubble parameter. We find consistency between the viscosity coefficient and the condition imposed by the second law of the Thermodynamics. The second part is dedicated to constrain the free parameter of the interacting viscous model (IVM) for three particular cases: the viscous model (VM), interacting model (IM), and the perfect fluid case (the concordance model). We report the deceleration parameter to be $q_0 = -0.54^{+0.06}_{-0.05}$, $-0.58^{+0.05}_{-0.04}$, $-0.58^{+0.05}_{-0.05}$, $-0.63^{+0.02}_{-0.02}$, together with the jerk parameter as $j_0 = 0.87^{+0.06}_{-0.09}$, $0.94^{+0.04}_{-0.06}$, $0.91^{+0.06}_{-0.10}$, $1.0$ for the IVM, VM, IM, and LCDM respectively, where the uncertainties correspond at 68\% CL. Worth mentioning that all the particular cases are in good agreement with LCDM, in some cases producing even better fits, with the advantage of eliminating some problems that afflicts the standard cosmological model.