The Hartle-Hawking wave function in 2d causal set quantum gravity

TL;DR

This paper defines and analyzes the Hartle-Hawking wave function within 2D causal set quantum gravity, revealing dominant non-continuum causal sets with unique geometric properties at low temperatures.

Contribution

It introduces a non-perturbative approach to the Hartle-Hawking wave function in 2D causal set theory using numerical methods, highlighting novel geometric features.

Findings

Dominance of non-continuum causal sets with rapid spatial expansion

High spatial homogeneity due to extensive causal past overlaps

Potential implications for quantum gravity's role in the universe

Abstract

We define the Hartle-Hawking no-boundary wave function for causal set theory (CST) over the discrete analogs of spacelike hypersurfaces. Using Markov Chain Monte Carlo and numerical integration methods we analyse the wave function in non- perturbative 2d CST. We find that in the low temperature regime it is dominated by causal sets which have no continuum counterparts but possess physically interesting geometric properties. Not only do they exhibit a rapid spatial expansion with respect to the discrete proper time but also a high degree of spatial homogeneity. The latter is due to the extensive overlap of the causal pasts of the elements in the final discrete hypersurface and corresponds to high graph connectivity. Our results thus suggest new possibilities for the role of quantum gravity in the observable universe.