Cosmological model involving an interacting van der Waals fluid

Abstract: A model for the late-time accelerated expansion of the universe is considered where a van der Waals fluid interacting with matter plays the role of dark energy. The transition towards this phase in the cosmic evolution history is discussed in detail and, moreover, a complete classification of the future finite-time singularities is obtained for six different possible forms of the non-gravitational interaction between dark energy (the van der Waals fluid) and dark matter. This study shows, in particular, that a universe with a non-interacting three-parameter van der Waals fluid can evolve into a universe characterized by a Type IV~(Generalized Sudden) Singularity. On the other hand, for certain values of the parameters, exit from the accelerated expanding phase is possible in the near future, what means that the expansion of the universe in the future could become decelerated. On the other hand, our study shows that space can be divided into different regions. For some of them, in particular, the non-gravitational interactions $Q = 3 H b \rho_{de}$, $Q = 3 H b \rho_{dm}$ and $Q = 3 H b (\rho_{de} + \rho_{de})$ may completely suppress future finite-time singularity formation, for sufficiently high values of $b$. On the other hand, for some other regions of the parameter space, the mentioned interactions would not affect the singularity type, namely the Type IV singularity generated in the case of the non-interacting model would be preserved. A similar conclusion has been archived for the cases of $Q = 3 b H \rho_{de}\rho_{dm}/(\rho_{de}+\rho_{dm})$, $Q = 3 b H \rho_{dm}^{2}/(\rho_{de}+\rho_{dm})$ and $Q = 3 b H \rho_{de}^{2}/(\rho_{de}+\rho_{dm})$ non-gravitational interactions, with only one difference: the $Q = 3 b H \rho_{dm}^{2}/(\rho_{de}+\rho_{dm})$ interaction will change the Type IV singularity of the non-interacting model into a Type II~(The Sudden) singularity.