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

Stephen L. Adler

TL;DR

The paper investigates a frame-dependent dark energy action that mimics a cosmological constant in FRW but alters scalar perturbations, leading to a one-parameter family of cosmologies. It develops both perturbative and non-perturbative approaches, finding close agreement and showing that the parameter θ(0) (or equivalently Φ(0)) governs deviations from standard FRW and the expansion history. The analysis yields modified cosmographic distances and an effective Hubble parameter, and demonstrates that with f=1 the model can alleviate the late-time Hubble tension by increasing the local H0 relative to the CMB value, though BAO constraints at intermediate redshifts may become challenging. The work thus provides a concrete late-time modification to cosmic expansion with testable implications for distance measures, BAO, and the age of the universe.

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.

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

TL;DR

The paper investigates a frame-dependent dark energy action that mimics a cosmological constant in FRW but alters scalar perturbations, leading to a one-parameter family of cosmologies. It develops both perturbative and non-perturbative approaches, finding close agreement and showing that the parameter θ(0) (or equivalently Φ(0)) governs deviations from standard FRW and the expansion history. The analysis yields modified cosmographic distances and an effective Hubble parameter, and demonstrates that with f=1 the model can alleviate the late-time Hubble tension by increasing the local H0 relative to the CMB value, though BAO constraints at intermediate redshifts may become challenging. The work thus provides a concrete late-time modification to cosmic expansion with testable implications for distance measures, BAO, and the age of the universe.

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.

Paper Structure

This paper contains 18 sections, 60 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Homogeneous isotropic metric, why the $f\neq 0$ case does not reduce to $f=0$, and some notations
  3. Why the $f \neq 0$ case cannot be reduced to $f=0$ by redefining the time variable
  4. Some notations
  5. Metric perturbation derivation
  6. Setting up the $\Phi$ equation
  7. Large and small $x$ behavior and numerical solution
  8. Non-perturbative derivation
  9. Einstein tensor and equations, and the dark energy and matter energy momentum tensors
  10. Einstein equations
  11. Finding the second equation
  12. Differential equation for $\theta$, reduction to the linearized case, and large and small time behavior
  13. Numerical solution
  14. Correspondence of the non-perturbative and perturbative solutions
  15. Cosmographic equations and application to the "Hubble tension"
  16. ...and 3 more sections