Some Research Of Modified Gravity Theories Based On Teleparallel Space-time

In this thesis, we explore some aspects of modified gravity theories based on teleparallel space-time.Firstly, we use the parameterized post-Newtonian (PPN) formalism to explore the weak field approximation of teleparallel gravity non-minimally coupling to a scalar field φ, with arbitrary coupling function ω(φ) and potential V(φ). We find that all the PPN parameters are identical to general relativity (GR), which makes this class of theories compatible with the Solar System observations. This feature also makes the theories quite different from the scalar-tensor theories, which may have stringent constraint on the parameter space or need some screening mechanisms to pass the Solar System’s experimental constraints.Secondly, inspired by the f(R) non-linear massive gravity, we propose a new kind of modified gravity model, namely f(T) non-linear massive gravity, by imposing the dRGT mass term reformulated in the vierbein formalism, to the f(T) theory. We then investigate the cosmological evolution of f(T) non-linear massive gravity. As a concrete example, we study the exponential type of f(T) massive gravity. We find that the exponential f(T) massive gravity can give an account for the late-time acceleration of our universe without resorting to dark energy (DE). Besides, the crossing of the phantom divide line from the non-phantom phase to the phantom one as the redshift decreases can be easily realized in this exponential...