Extended teleparallel cosmology

Abstract

Over the last 100 years General Relativity (GR) has been an extremely successful theory of gravity and also considered as a fundamental theory. GR has been extensively used to study the Universe, however it turned out that it is not a complete theory as more observations were available. This resulted in GR not being able to explain Dark Energy (DE) and Dark Matter (DM), assuming that these are the missing components in explaining the late time cosmology. Incorporating DE and cold DM into GR, the ΛCDM model was created that solved most of observational cosmological problems. So far, DE and DM although kind of natural hypotheses, are not globally accepted concepts and have not been directly observed. On top of that there is a new sector of cosmology called gravitational wave astronomy which is based on the dynamics of gravitational waves and the plethora of relevant datasets that can be immediately used to constrain gravitational models. All the aforementioned problems serve only part of the reasons that lead to modify GR. The process of modifying GR is not that simple. At times this can lead to solving problems but also creating new ones. As such in depth studies of these modified theories must be always performed. From these studies a lot of useful insights were gained regarding the foundations and cosmology of GR. It should be noted that Einstein himself first modified GR in an attempt to unify electromagnetism with gravity via torsion by setting curvature to zero. This is exactly the birth of teleparallel theories of gravity (TG). In this thesis, the TG framework is introduced starting from its motivation to its technical details and how to modify it. Moreover, the teleparallel analogue of Horndeski theory is presented and probed against multimessenger events of GW170817 [5] and GRB170817A [6]. Its polarization modes and degrees of freedom are also extensively studied and compared with Horndeski theory. In this direction the f(T, B) gravity is also probed against the multimessenger events and in general studied perturbatively in the cosmological background. Finally, a version of a teleparallel equivalent of the generalised Proca theories is constructed and its Friedmann equations are calculated as a first application to cosmology.