Future singularities arising in a family of models for the expanding universe, characterized by sharing a convenient parametrization of the energy budget in terms of the deceleration parameter, are classified. Finite-time future singularities are known to appear in many cosmological scenarios, in particular, in the presence of viscosity or nongravitational interactions, the last being known to be able to suppress or just change in some cases the type of the cosmological singularity. Here, a family of models with a parametrization of the energy budget in terms of the deceleration parameter are studied in the light of Gaussian processes using reconstructed data from [Formula: see text]-value [Formula: see text] datasets. Eventually, the form of the possible nongravitational interaction between dark energy and dark matter is constructed from these smoothed [Formula: see text] data. Using phase space analysis, it is shown that a noninteracting model with dark energy [Formula: see text] ([Formula: see text] being the deceleration parameter) may evolve, after starting from a matter-dominated unstable state, into a de Sitter universe (the solution being in fact a stable node). Moreover, for a model with interaction term [Formula: see text] ([Formula: see text] is a parameter and [Formula: see text], the Hubble constant) three stable critical points are obtained, which may have important astrophysical implications. In addition, part of the paper is devoted to a general discussion of the finite-time future singularities obtained from direct numerical integration of the field equations, since they appear in many cosmological scenarios and could be useful for future extended studies of the models here introduced. Numerical solutions for the new models, produce finite-time future singularities of Type I or Type III, or an [Formula: see text]-singularity, provided general relativity describes the background dynamics.
The future of the universe in modified gravitational theories: approaching a finite-time future singularity