Dynamical dark energy and infinite statistics

In the ACDM model, dark energy is viewed as a constant vacuum energy density, the cosmological constant in the Einstein-Hilbert action. This assumption can be relaxed in various models that introduce a dynamical dark energy. In this paper, we argue that the mixing between infrared (IR) and ultraviolet (UV) degrees of freedom in quantum gravity leads to infinite statistics, the unique statistics consistent with Lorentz invariance in the presence of nonlocality, and yields a fine structure for dark energy. Introducing IR and UV cutoffs into the quantum gravity action, we deduce the form of A as a function of redshift and translate this to the behavior of the Hubble parameter.