Date of Award
8-23-2024
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Physics
Advisor(s)
Jack Laiho
Second Advisor
Monica Deza
Keywords
Dark Energy;Lattice;Quantum Gravity
Subject Categories
Physical Sciences and Mathematics | Physics
Abstract
We study various topics of Euclidean dynamical triangulations (EDT). We study the interaction of two scalar particles, and show that in the appropriate limit we recover an interaction compatible with Newton's gravitational potential in four dimensions. Working in the quenched approximation, we calculate the binding energy of a two-particle bound state, and study its dependence on the constituent particle mass in the non-relativistic limit. We find a binding energy compatible with the ground state energy by solving the Schr\"{o}dinger equation for Newton's potential. This allows us to determine the lattice spacing in EDT for the first time, and we find that our lattice spacings are smaller than the Planck length, suggesting that we can achieve a separation of scales and that there is no obstacle to taking a continuum limit. We also introduce a new algorithm for the simulation of EDT that mimics the Metropolis-Hastings algorithm, but where all proposed moves are accepted. This rejection-free algorithm can efficiently simulate theories with global terms, while still maintaining detailed balance. We test our algorithm on the $2d$ Ising model, and against results for EDT obtained with Metropolis. Our new algorithm allows us to generate finer EDT lattices than previously possible, and we find geometries that resemble semiclassical Euclidean de Sitter space in agreement with earlier results at coarser lattices. The agreement between lattice data and the classical de Sitter solution continues to get better as lattice spacing decreases. We then study the dark energy on EDT lattices. We find that it behaves like a cosmological constant with a correction term that contains dynamics that varies with time, and can be described as a linear function. The constant part allows us to determine the ratio between direct and dual lattice spacing more accurately, and the parameter of the dynamic part ($\nu$) has consistent behavior across lattice spacings. We calculate the real world value of $\nu$ in the quenched approximation, and discuss the small modifications it makes to the prediction of $\Lambda$CDM model.
Access
Open Access
Recommended Citation
Dai, Mingwei, "Dynamical Dark Energy from Lattice Quantum Gravity" (2024). Dissertations - ALL. 1989.
https://surface.syr.edu/etd/1989
