Combinatorial Dark Energy

TL;DR

This paper proposes a model where dark energy arises from a small negative residual scalar curvature in discrete spacetime, explaining the observed small positive cosmological constant through entropic forces and microstate counting.

Contribution

It introduces a discrete spacetime model linked to quantum gravity that naturally accounts for dark energy and the small positive cosmological constant.

Findings

Numerical evidence suggests microstates increase as curvature decreases.

The model predicts a small negative residual curvature in empty spacetime.

Estimated cosmological constant aligns with observed tiny positive value.

Abstract

In this paper, we give a conceptual explanation of dark energy as a small negative residual scalar curvature present even in empty spacetime. This curvature ultimately results from postulating a discrete spacetime geometry, very closely related to that used in the dynamical triangulations approach to quantum gravity. In this model, there are no states which have total scalar curvature exactly zero. Moreover, numerical evidence in dimension three suggests that, at a fixed volume, the number of discrete-spacetime microstates strongly increases with decreasing curvature. Because of the resulting entropic force, any dynamics which push empty spacetime strongly toward zero scalar curvature would instead produce typically observed states with a small negative curvature. This provides a natural explanation for the empirically observed small positive value for the cosmological constant (Lambda is about 10^(-121) in Planck units.) In fact, we derive the very rough estimate Lambda=10^(-187) from a simple model containing only the two (highly-degenerate) quantum states with total scalar-curvature closest to zero.