Dark Energy And F(T) Gravity

We investigate both the coincidence problem of dark energy and modifedtheory of gravity, f (T) gravity, in this dissertation.In study of the coincidence problem, we fnd the equivalence between twodiferent types of triple interacting dark energy models. We also get the concretetransfer terms between diferent energy components by studying the stationarysituation, and fnd that three groups of solutions will be get by mathematicalcalculation, but only one of them is compatible with the data of observations. Inthe scenario described by this group of solution, matter, including dark matterand baryonic matter, receives energy from dark energy and decays into radiation,which protects the balance between diferent energy components and resolvesthe triple coincidence problem. Then, we investigate the stability of the tripleinteracting dark energy model in detail, the complete table of relations betweenthe stability and the transfer terms is given. We fnd that only models withtransformation between matter and dark energy proportional to ρcor ρDE, whilethe transformation between radiation and matter is not proportional to ρR, arestable against perturbation, which give strong restriction on the model buildingof the triple interacting.In study of f (T) gravity, we reconstruct the f (T) gravity according to holo-graphic energy models. f (T) gravity is a modifed theory of teleparallel gravity,and energy density of holographic energy models is always defned by geomet-rical objects. Their common relations to geometry of the spacetime have in-spired recent eforts of reconstructing f(T) gravities, which can accommodate anaccelerated universe, from holographic dark energy models. Apparently, difer-ent holographic energy models will lead to diferent f (T) gravities, we do our reconstruction according three holographic dark energy models in various timedurations; we also make the reconstruction according to the model established byourselves, the holographic ρKM Rmodel. By using the boundary conditions whichare used in many references, we fnd that the present boundary conditions causesome problem in the reconstruction, such as one cannot see the expected behav-iors of rescaling of the theory. This is caused by the boundary conditions whichare not inaccurate enough. We propose new boundary conditions and fnd thatmore reasonable results will be get when one uses the new boundary conditions.