Narrow Results

In earlier work we showed that a frame dependent effective action motivated by the postulates of three-space general coordinate invariance and Weyl scaling invariance exactly mimics a cosmological constant in Robertson–Walker (RW) spacetimes. Here we study the implications of this effective action for small fluctuations around a spatially flat RW background geometry. The equations for the conserving extension of the modified stress-energy tensor can be integrated in closed form, and involve only the metric perturbation $h_{00}$. Hence the equations for tensor and vector perturbations are unmodified, but there are Hubble scale additions to the scalar perturbation equations, which nonetheless admit no propagating wave solutions. Consequently, there are no modifications to standard gravitational wave propagation theory, but there may be observable implications for cosmology. We give a self-contained discussion, including an analysis of the restricted class of gauge transformations that act when a frame dependent effective action is present.

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 $\mathrm{\Phi }$ 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 $\mathrm{\Lambda }\mathrm{\text{CDM}}$ cosmology. We also give new analytic results for the function $\mathrm{\Phi }$ and discuss their implications.