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.
