#### Date of Award

December 2019

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics

#### Advisor(s)

John W. Laiho

#### Second Advisor

Graham J. Leushke

#### Keywords

Dynamical, Euclidean, Gravity, Lattice, Quantum, Triangulations

#### Subject Categories

Physical Sciences and Mathematics

#### Abstract

Quantum field theories have been incredibly successful at describing many fundamental aspects of reality with great precision, sometimes relying on the powerful computational tool of lattice methods. Gravity has so far eluded a quantum field theory description, leading many to consider alternate theories like String Theory. However, recent results in lattice quantum gravity have brought some renewed interest in the subject. After reviewing the progress made so far in Euclidean Dynamical Triangulations, a lattice theory of gravity, we examine how the couplings of the theory run with scale. We find that the dimensionless couplings $\hat{G}$ and $\hat{\Lambda}$ are not separately relevant, but $G\Lambda$ is. We argue that the lattice regulator breaks general coordinate invariance, and so a parameter must be fine tuned to restore this symmetry. $\beta$ is that parameter. Once the non-physical contribution to the running of the couplings is subtracted, the correct infrared behavior is recovered, and the relevant coupling appears to approach a fixed point in the ultraviolet. With only one relevant coupling, the theory is maximally predictive, requiring only a single dimensionful input to set the lattice scale, and all other quantities become predictions of the model. We also study two-point curvature correlation functions for gravity. Upon removing the disconnected contributions to the correlators, we find universal behavior in these correlators, including a power-law drop-off with distance with a power consistent with -10. We also explore a means to extract the coefficient of the $R^2$ term in the low energy effective action. We find that this coefficient may be very large in magnitude, though a calculation in the low energy effective theory is still needed to test this possibility. This result may imply that the Starobinsky Model of inflation emerges from our theory. If these results hold up under further scrutiny, it could have important implications for observational cosmology.

#### Access

Open Access

#### Recommended Citation

Bassler, Scott David, "Euclidean Dynamical Triangulations: Running Couplings and Curvature Correlation Functions" (2019). *Dissertations - ALL*. 1104.

https://surface.syr.edu/etd/1104