A Reasonable Ab Initio Cosmological Constant Without Holography

We give a well-motivated explanation for the origin of dark energy, claiming that it arises from a small residual negative scalar-curvature present even in empty spacetime. The vacuum has this residual curva-ture because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect in the well-known dynamical triangu-lations (DT) model for quantum gravity and the predicted cosmological constant Λ agrees with observation. We begin by almost completely characterizing the DT-model’s vac-uum energies in dimension three. Remarkably, the energy gap between states comes in increments of ∆A = ` 8V in natural units, where ` is the “Planck length ” in the model and V is the volume of the universe. Then, using only vacua in the N energy levels nearest zero, where N is the universe’s radius in units of `, we apply our model to the current co-moving spatial volume to get |Λ | ≈ 10−123. This result comes with a rigorous proof and does not depend on any holographic principle or carefully tuned parameters. Our only unknown is the relative entropy of the low-energy states, which sets the sign of Λ. Numerical evidence strongly suggests that spacetime entropy in the DT-model is a decreasing function of scalar-curvature, so the model also predicts the correct sign for Λ. 1 a