| Summary: | Our theoretical understanding of the dynamical evolution of the Universe has certainly improved during the recently established era of precision cosmology. However, the nature of the dark sector remains the greatest puzzle in cosmology. Although we re–establish that the concordance model of cosmology is in agreement with current cosmological observations, this simplistic model is unequivocally theoretically unappealing. Thence, we investigate a number of alternative cosmological models and illustrate their distinctive cosmological consequences. For instance, we consider a scalar–tensor theory of gravitation, such that the minimally coupled scalar field is explicitly coupled to multiple fluid components. The assumed coupling functions are specified by the theoretically well–motivated conformal and disformal coupling functions. We perform a dynamical systems analysis, in which we establish the existence and stability conditions for every fixed point, and illustrate that disformally coupled systems have a dissimilar cosmological evolution with respect to the conformally coupled and uncoupled systems. We further show that a disformal coupling between the matter and radiation sectors is characterised by a varying fine–structure constant. Moreover, a direct coupling between dark energy and dark matter is not theoretically forbidden and might be incorporated in extensions of the standard model of particle physics. We consider a coupled quintessence model, in which the dark energy scalar field only couples to dark matter via the conformal and disformal coupling functions, and is decoupled from the conventional baryonic matter sector. We scrutinise the distinctive features of this cosmological model, where we particularly show that when the dark sector constituents are disformally coupled, intermediate–scales and time–dependent damped oscillations appear in the matter growth rate function. We confront this coupled quintessence model with current cosmological data sets, and illustrate that Nature is consistent with a null coupling within the dark sector of the Universe.
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