High Performance Algorithms for Quantum Gravity and Cosmology

TL;DR

This paper introduces high-performance algorithms optimized for large-scale numerical experiments in theoretical physics, specifically applied to quantum gravity, cosmology, and string theory, significantly reducing simulation runtimes.

Contribution

It presents the most compact and efficient algorithms for representing and analyzing systems modeled by sets or graphs, with applications to causal set quantum gravity and multiverse cosmology.

Findings

Optimized algorithms for causal set action calculation

New solutions for geodesic equations in FLRW spacetimes

Reduced simulation runtimes by orders of magnitude

Abstract

Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or graphs. After studying how these implementations maximize instruction throughput and optimize memory access patterns, we apply them to causal set quantum gravity, in which spacetime is represented by a partially ordered set. We build upon the low-level set and graph algorithms to optimize the calculation of the causal set action, and then discuss how to measure boundaries of a discrete spacetime. We then examine the broader applicability of these algorithms to greedy information routing in random geometric graphs embedded in Lorentzian manifolds, which requires us to find new closed-form solutions to the geodesic differential equations in Friedmann-Lemaitre-Robertson-Walker spacetimes. Finally, we consider the vacuum selection problem in string theory, where we show a network-centered approach yields a dynamical mechanism for vacuum selection in the context of multiverse cosmology. These algorithms have broad applicability to many physical systems, and they improve existing methods by reducing simulation runtimes by orders of magnitude.