Effective Dark Energy Models and Dark Energy Models with Bounce in frames of $F(T)$ Gravity

Abstract: Various cosmological models in frames of $F(T)$ gravity are considered. The general scheme of constructing effective dark energy models with various evolution is presented. It is showed that these models in principle are compatible with $\Lambda$CDM model. The dynamics of universe governed by $F(T)$ gravity can mimics $\Lambda$CDM evolution in past but declines from it in a future. We also construct some dark energy models with the "real" (non-effective) equation-of-state parameter $w$ such that $w\leq-1$. It is showed that in $F(T)$ gravity the Universe filled phantom field not necessarily ends its existence in singularity. There are two possible mechanisms permitting the final singularity. Firstly due to the nonlinear dependence between energy density and $H^{2}$ ($H$ is the Hubble parameter) the universe can expands not so fast as in the general relativity and in fact Little Rip regime take place instead Big Rip. We also considered the models with possible bounce in future. In these models the universe expansion can mimics the dynamics with future singularity but due to bounce in future universe begin contracts.