Foundational Investigations & Astronomical Implications of Quantum Gravity

In this thesis we consider foundational elements of quantum gravity as well as it possible observable astrophysical effects. In particular investigate a background independent formulation of Matrix Theory. We discuss a background independent formulation of a holographic theory of quantum gravity. The present thesis incorporates the necessary background material on geometry of canonical quantum theory, holography and spacetime thermodynamics, Matrix theory, as well as our specific proposal for a dynamical theory of geometric quantum mechanics, as applied to Matrix theory. At the heart of this thesis is a new analysis of the conceptual problem of time and the closely related and phenomenologically relevant problem of vacuum energy in quantum gravity. We also present a discussion of some observational implications of this new viewpoint on the problem of vacuum energy. as well as a novel solution to the low entropy and arrow of time puzzles of the initial state of the Universe. Our approach derives from the physics of the specific generalization of Matrix theory as the basis for a quantum theory of gravity considered here. The particular dynamical state space of this theory, the infinite dimensional analogue of the Fubini-Study metric over a complex non-linear Grassmannian, has recently been studied by Michor and Mumford. The geodesic distance between any two points on this space is zero. Here we show that this mathematical result translates to a description of a hot, zero entropy state and an arrow of time after the Big Bang. This is modeled as a far from equilibrium, large fluctuation driven, "freezing by heating" metastable ordered phase transition of a non-linear dissipative dynamical system. We also consider an evaporating black hole in the presence of an extra spatial dimension would undergo an explosive phase of evaporation. We show that such an event, involving a primordial black hole, can produce a detectable, distinguishable electromagnetic pulse, signaling the existence of an extra dimension of size L â ¼ 10â 18 â 10â 20 m. We derive a generic relationship between the Lorentz factor of a pulse-producing "fireball" and the TeV energy scale. For an ordinary toroidally compactified extra dimension, transient radio-pulse searches probe the electroweak energy scale (â ¼0.1 TeV), enabling comparison with the Large Hadron Collider.