Executive Summary : | The late Universe is fairly well understood in the context of the numerous surveys and observations that have taken place in that regime of cosmic history. However, access to early Universe physics continues to pose many open questions such as the nature of inflation and the physics that may have been at play at the very earliest epochs of cosmology. The cosmic microwave background (CMB) radiation gives us a glimpse of the earliest times at which the Universe allowed photons to flow freely. Bouncing cosmologies offer a path to describe the earliest epochs of the Universe by proposing various scenarios in which the Hubble parameter is analytic up to the earliest times of cosmic evolution. This physics can be directly connected with novel expressions of exotic matter as well as modifications to standard gravity. These modifications have recently become more important due to their potential to explain the growing issue of cosmic tensions which stems from divergences in a growing list of cosmological parameters when determined using either late time data sets or observations from the early Universe such as the CMB. In this project, we intend to explore the phenomenology of a number of modified theories of gravity in the very early Universe and to investigate their possible consequences in the context of bouncing cosmologies. While modified theories of gravity are degenerate in the late Universe, there is significant amount of distinction in the early Universe. One particularly interesting approach to modified theories of gravity is teleparallel gravity(TG) in which the curvature associated with the Levi-Civita connection is exchanged with the torsional teleparallel connection. This has led to new gravity in which novel phenomenology has become possible. Some work has been carried out in nonminimally coupled extensions to standard gravity, which has already shown promising results in which the early Universe singularity can be averted using particular choices of the gravitational mode. These have also been shown to be compatible with some late time data surveys. TG can be formulated to produce a dynamically equivalent of general relativity albeit with different expressions due to the use of different connections. This approach to gravity results in the Ricci scalar being expressed as a dynamical part as well as a total divergence contribution (which is the reason why regular modified gravity immediately results in fourth-order theories ). Another approach to teleparallel bouncing cosmologies has been explored through modifications to standard gravity in which the dynamical and total divergence contributions are allowed to vary freely. Some results were found in terms of the allowable forms of the gravitational Lagrangian model. We will produce new works on the topic of early Universe physics in the regime of teleparallel cosmology with the aim of producing models that are viable both at early times while also agreeing with surveys at later times. |