Hubble parameter and related formulas for a Weyl scaling invariant dark energy action

We extend our previous analysis of a model for "dark energy" based on a Weyl scaling invariant dark energy action. We reexpress all prior results in terms of proper time, using the fluctuation amplitude $\Phi$ without approximation, and derive a compact formula for the squared effective Hubble parameter. This formula involves effective dark energy and matter densities that differ from their expressions in the standard $\Lambda CDM$ cosmology. We also give new analytic results for the function $\Phi$ and discuss their implications.