In this paper, after reconstructing the redshift evolution of the Hubble function by adopting Gaussian process techniques, we estimate the best-fit parameters for some flat Friedmann cosmological models based on a modified Chaplygin gas interacting with dark matter. In fact, the expansion history of the Universe will be investigated because passively evolving galaxies constitute cosmic chronometers. An estimate for the present-day values of the deceleration parameter, adiabatic speed of sound within the dark energy fluid, effective dark energy, and dark matter equation of state parameters is provided. By this, we mean that the interaction term between the two dark fluids, which breaks the Bianchi symmetries, will be interpreted as an effective contribution to the dark matter pressure similarly to the framework of the “Generalized Dark Matter”. We investigate whether the estimates of the Hubble constant and of the present-day abundance of dark matter are sensitive to the dark matter–dark energy coupling. We will also show that the cosmic chronometers data favor a cold dark matter, and that our findings are in agreement with the Le Châtelier–Braun principle according to which dark energy should decay into dark matter.

In this paper, applying the Hartman–Grobman theorem we carry out a qualitative late-time analysis of some unified dark energy-matter Friedmann cosmological models, where the two interact through linear energy exchanges, and the dark energy fluid obeys to the dynamical equation of state of Redlich–Kwong, Modified Berthelot, and Dieterici respectively. The identification of appropriate late-time attractors allows to restrict the range of validity of the free parameters of the models under investigation. In particular, we prove that the late-time attractors which support a negative deceleration parameter correspond to a de Sitter universe. We show that the strength of deviation from an ideal fluid for the dark energy does not influence the stability of the late-time attractors, as well as the values of all the cosmological parameters at equilibrium, but for the Hubble function (which represents the age of the universe). Our analysis also shows that a singularity in the effective equation of state parameter for the dark energy fluid is not possible within this class of models.

We examine the effect that the magnetic part of the Weyl tensor has on the large-scale expansion of space. This is done within the context of a class of cosmological models that contain regularly arranged discrete masses, rather than a continuous perfect fluid. The natural set of geodesic curves that one should use to consider the cosmological expansion of these models requires the existence of a non-zero magnetic part of the Weyl tensor. We include this object in the evolution equations of these models by performing a Taylor series expansion about a hypersurface where it initially vanishes. At the same cosmological time, measured as a fraction of the age of the universe, we find that the influence of the magnetic part of the Weyl tensor increases as the number of masses in the universe is increased. We also find that the influence of the magnetic part of the Weyl tensor increases with time, relative to the leading-order electric part, so that its contribution to the scale of the universe can reach values of \(\sim \)1%, before the Taylor series approximation starts to break down.