Study of finite-time singularities of loop quantum cosmology interacting multifluids

In this work we study the occurrence of finite-time cosmological singularities in a cosmological system comprising three fluids. Particularly, the system contains two dark fluids, namely, that of dark energy and dark matter, which are interacting, and of a noninteracting baryonic fluid. For the study we adopt the phase space approach by constructing the cosmological dynamical system in such a way that it is rendered as an autonomous polynomial dynamical system, and in order to achieve this, we appropriately choose the variables of the dynamical system. By employing a rigid mathematical framework, that of dominant balances analysis, we demonstrate that there exist nonsingular solutions of the dynamical system, which correspond to a general set of initial conditions, which proves that no big rip or type III finite-time singularities occur in this loop quantum cosmology multifluid dynamical system. Thus the new feature of this work is that we are able to do this using an analytic technique instead of adopting a numerical approach. In addition, we perform a fixed point analysis of the cosmological dynamical system, and we examine the behavior of the total effective equation of state parameter, at the fixed points, as a function of the free parameters of the system. Finally, we investigate the phenomenological implications of the dark energy equation of state, which we assumed governs the dark energy fluid.