2012/08/15 by Aaron Trout, Aaron D. Trout, Trout, Aaron D.
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1208.3186
1 Figure
arxiv created 2012/08/15 · openalex publication_date 2012/08/15 · arxiv updated 2012/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 curvature 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 \em dynamical triangulations (DT) model for quantum gravity and the predicted cosmological constant Λ agrees with observation. We begin by almost completely characterizing the DT-model's vacuum energies in dimension three. Remarkably, the energy gap between states comes in increments of [ΔA =(ℓ)/(8V)] in natural units, where ℓ 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 ℓ, 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.