f(T) teleparallel gravity and cosmology

Over the past decades, the role of torsion in gravity has been extensivelyinvestigated along the main direction of bringing gravity closer to its gaugeformulation and incorporating spin in a geometric description. Here we reviewvarious torsional constructions, from teleparallel, to Einstein-Cartan, andmetric-affine gauge theories, resulting in extending torsional gravity in theparadigm of f(T) gravity, where f(T) is an arbitrary function of the torsionscalar. Based on this theory, we further review the corresponding cosmologicaland astrophysical applications. In particular, we study cosmological solutionsarising from f(T) gravity, both at the background and perturbation levels, indifferent eras along the cosmic expansion. The f(T) gravity construction canprovide a theoretical interpretation of the late-time universe acceleration,and it can easily accommodate with the regular thermal expanding historyincluding the radiation and cold dark matter dominated phases. Furthermore, ifone traces back to very early times, a sufficiently long period of inflationcan be achieved and hence can be investigated by cosmic microwave backgroundobservations, or alternatively, the Big Bang singularity can be avoided due tothe appearance of non-singular bounces. Various observational constraints,especially the bounds coming from the large-scale structure data in the case off(T) cosmology, as well as the behavior of gravitational waves, are describedin detail. Moreover, the spherically symmetric and black hole solutions of thetheory are reviewed. Additionally, we discuss various extensions of the f(T)paradigm. Finally, we consider the relation with other modified gravitationaltheories, such as those based on curvature, like f(R) gravity, trying toenlighten the subject of which formulation might be more suitable forquantization ventures and cosmological applications

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

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions