  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.
