Universe From Scratch: Exploring Quantum Gravity in 2+1 Dimensions using the Causal Dynamical Triangulation Method

Prakrit Shrestha

2014

Quantum Gravity is a field of physics that attempts to describe gravity according to the principles of quantum mechanics. A potentially powerful approach to quantum gravity is Causal Dynamical Triangulations (CDT). CDT is a modification of quantum Regge calculus where spacetime is discretized and approximated using multi-dimensional triangles called simplices. This thesis implements a (2+1) dimensional toy model of our (3+1) dimensional universe. Its goal is to provide an introduction to quantum gravity and to expand the computational and analytical understanding of this model. It examines the topology of spacetime including concepts of general relativity and quantum mechanics. It generalizes Feynman's path integral to a sum over spacetime geometries characterized by the Einstein-Hilbert action. The topological structure of spacetime carries a Lorentzian signature and is distorted to obtain varying geometry by performing a set of Lorentzian Monte-Carlo moves. Finally, it describes the design, construction, operation and future work of a computer simulation of a 2 + 1 dimensional CDT universe.