Teleparallel gravity and its modifications

The teleparallel equivalent of general relativity is an intriguing alternative formulation of general relativity. In this thesis, we examine theories of teleparallel gravity in detail, and explore their relation to a whole spectrum of alternative gravitational models, discussing their position within the hierarchy of Metric Affine Gravity models. Consideration of alternative gravity models is motivated by a discussion of some of the problems of modern day cosmology, with a particular focus on the dark energy problem. Modifications of gravity in the teleparallel framework are examined as potential models to alleviate some of these issues and the relationships between various teleparallel and non-teleparallel modified gravity models are analysed in depth. In particular f(T,B) gravity, where T is a torsion scalar and B is a derivative of a torsion vector, is introduced as a way of analysing both f(T ) gravity and f(R) gravity, where R is the Ricci scalar, within the same unified framework. Various theoretical issues of all of these theories are discussed. In a similar way, teleparallel scalar-tensor models are analysed, taking into account coupling between torsion and a scalar field, with dynamical systems techniques utilised to analyse the cosmology of these models. An interesting conformal relationship is found to hold between teleparallel scalar-tensor models and f(T,B) gravity. Primary Supervisor: Dr Christian Böhmer