  In the $\Lambda$CDM 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 letter, we argue that the mixing between infrared and
ultraviolet degrees of freedom in quantum gravity lead to infinite statistics,
the unique statistics consistent with Lorentz invariance in the presence of
non-locality, and yield a fine structure for dark energy. Introducing IR and UV
cutoffs into the quantum gravity action, we deduce the form of $\Lambda$ as a
function of redshift and translate this to the behavior of the Hubble
parameter.
