Implications of a frame dependent dark energy for the spacetime metric, cosmography, and effective Hubble constant

Abstract: In earlier papers 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 Friedmann-Robertson-Walker (FRW) spacetimes, but alters the linearized equations governing scalar perturbations around a spatially flat FRW background metric. Here we analyze the implications of a frame dependent dark energy for the spacetime cosmological metric within both a perturbative and a non-perturbative framework. Both methods of calculation give a one-parameter family of cosmologies which are in close correspondence to one another, and which contain the standard FRW cosmology as a special case. We discuss the application of this family of cosmologies to the standard cosmological distance measures and to the effective Hubble parameter, with special attention to the current tension between determinations of the Hubble constant at late time, and the Hubble value obtained through the cosmic microwave background (CMB) angular fluctuation analysis.