Cosmological predictions of scalar-tensor theories in teleparallel gravity

Abstract

The cosmological tensions following observational analysis as well as the late-time cosmic accelerated expansion provide a solid motivation for the adequacy of General Relativity as the primary theory for describing gravity. Under that novel viewpoint, scalar-tensor theories are commonly utilized as the typical method for investigating potential deviations from the ΛCDM model. Scalar-tensor theories are among the most extensively examined topics of modified gravity since their dynamical analysis reveals quite interesting behaviour associated with the various eras of cosmic evolution. The capacity of scalar-tensor theories to elucidate different cosmological epochs validates the increasing interest of the scientific community in the Horndeski theory of gravity, which is considered the most general scalar-tensor theory resulting in second-order field equations. The revival of the Horndeski theory in its contemporary form has generated profound research beyond the standard model of cosmology involving the broader framework of scalartensor theories. Following the detection of the GW170817 event, the constraints imposed on the terms of the Horndeski Lagrangian served as a starting point for its incorporation into Teleparallel Gravity. This results in the Teleparallel Analogue of Horndeski theory, known as the BDLS theory, which is discussed in the current thesis, followed by the classification of its models using the Noether Symmetry Approach. The investigation of the BDLS cosmological perturbations is also included along with their potential for further research on whether the No-go argument could be circumvented in a healthy manner. Furthermore, the Einstein Gauss-Bonnet model is examined by utilizing a dynamical system approach. This scalar-tensor theory contains a highly diverse phase space due to the inclusion of the fourth-order Gauss-Bonnet invariant combined with the second-order scalar field contribution. The critical points that emerge have the potential to enhance our comprehension of cosmic evolution as they differ noticeably compared to those already present in the literature.