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

TL;DR

This paper refines a Weyl scaling invariant dark energy model by deriving a new formula for the Hubble parameter and analyzing the effective densities, offering insights beyond standard cosmology.

Contribution

It provides a reexpression of previous results in terms of proper time and derives a compact formula for the squared effective Hubble parameter in the Weyl invariant dark energy model.

Findings

Derived a compact formula for the squared effective Hubble parameter.

Reexpressed all prior results using proper time and fluctuation amplitude.

Provided new analytic results for the function  and discussed implications.

Abstract

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.