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

We define the Hartle-Hawking no-boundary wave function for causal set quantum gravity over the discrete analogs of spacelike hypersurfaces. Using Markov Chain Monte Carlo and numerical integration methods we analyse this wave function in non-perturbative 2d causal set quantum gravity. Our results provide new insights into the role of quantum gravity in the observable universe. We find that non-manifold contributions to the Hartle-Hawking wave function can play a significant role. These discrete geometries exhibit a rapid spatial expansion with respect to the proper time and also possess a spatial homogeneity consistent with our current understanding of the observable universe. The Hartle-Hawking (HH) prescription for the ground state wave function over spatial closed 3-geometries (Σ, h) is the Euclidean functional integral over 4-geometries (M, g) Ψ0(hab,Σ) = A