Modified teleparallel theories of gravity

Teleparallel gravity is an alternative formulation of gravity which has the same field equations as General Relativity (GR), therefore, it is also known as the Teleparallel equivalent of General Relativity (TEGR). This theory is a gauge theory of the translations with the torsion tensor being non-zero but with a vanishing curvature tensor, hence, the manifold is globally flat. An interesting approach for understanding the late-time accelerating behaviour of the Universe is called modified gravity where GR is extended or modified. In the same spirit, since TEGR is equivalent to GR, one can consider its modifications and study if they can describe the current cosmological observations. This thesis is devoted to studying several modified Teleparallel theories of gravity with emphasis on late-time cosmology. Those Teleparallel theories are in general different to the modified theories based on GR, but one can relate and classify them accordingly. Various Teleparallel theories are presented and studied such as Teleparallel scalar-tensor theories, quintom models, Teleparallel non-local gravity, and f(T,B) gravity and its extensions (coupled with matter, extensions of new GR and Gauss-Bonnet) where T is the scalar torsion and B is the boundary term which is related with the Ricci scalar via R=-T+B.

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