Phase space of multi-fluid universe in $F(T)$-gravity and some enhancements for the oscillating interaction model

Abstract: Recently, a Friedmann-Robertson-Walker universe filled with various cosmological fluids has been considered by S.D. Odintsov et al. in [30] from phase space vantage point where various expressions for the Equation-of-State (EoS) parameter were studied. Since these types of EoS parameters are generative of appreciable results in the Hilbert-Einstein model, hence we intend to investigate all the cases in a homogeneous $F(T)$-gravity ($T$ is the torsion) through phase space analysis in precise detail. In short, three viable models of interaction between dark matter and dark energy, including usual-type, power-law type, and oscillating type, are investigated comprehensively. It is indicated that the power-law interaction in the related dynamical systems should be of increasing nature with time to get more critical points. Due to the failure of the oscillating model of ref. [30] in $F(T)$-gravity, four modified models are suggested and examined in both $F(T)$ and Hilbert-Einstein models. As to be seen, the modified models not only are generative of critical points equivalent to that of ref. [30], but also give rise to further critical points covering crucial stages of the evolution of the universe. In the context of these four models, such as the old one, at early times the interactions are negligible and they commence to grow as the cosmic time approaches the late-time in which the unification of early inflation and late acceleration is obtained. Using an indirect method, it is shown that the oscillating models have substantial roles in transitions between eras.