We will discuss non-local solutions to some of the problems of the standard model of cosmology, L cold dark matter (LCDM), focusing on two models of gravity and their applications to cosmology. The...Show moreWe will discuss non-local solutions to some of the problems of the standard model of cosmology, L cold dark matter (LCDM), focusing on two models of gravity and their applications to cosmology. The first comes from modifying the Einstien-Hilbert action by including an m2R 1 2 R term and the second by including an m2 1 R term. Both models posses self-accelerating solutions. I will demonstrate that their background cosmology is consistent with data, and testable primarily through the equation of state of our universe’s effective stress-energy tensor. At the perturbative level, these models have more galaxy clustering and weak lensing, so they are be highly testable using up coming cosmological surveys. My contribution to this work is the perturbation theory of the m2 1 R model and the recovery of these results for the m2R 1 2 R model.Show less
The main subject of this thesis is a reformulation of Einstein’s equation. In this reformulation, the variable is not a metric, but a connection on a vector bundle. Nevertheless, we can associate a...Show moreThe main subject of this thesis is a reformulation of Einstein’s equation. In this reformulation, the variable is not a metric, but a connection on a vector bundle. Nevertheless, we can associate a Riemannian metric to a connection. This allows us to relate the new formulation to the usual formulation, i.e. this allows us to argue that the new formulation is in fact a reformulation of Einstein’s equation. Since the physically significant metrics are of Lorentzian signature, we also consider modifying the new formulation in an attempt to make it suitable for Lorentzian metrics.Show less
