Inconsistencies from a Running Cosmological Constant

TL;DR

This paper investigates whether a scale-dependent cosmological constant can be consistent with general covariance in quantum gravity, concluding it cannot unless covariance is broken by regularization.

Contribution

The study systematically analyzes multiple approaches and demonstrates that a running cosmological constant violates general covariance unless explicitly broken.

Findings

A scale-dependent cosmological constant is incompatible with general covariance.

Regularization procedures tend to break covariance, allowing the cosmological constant to run.

Results have implications for quantum gravity and vacuum energy models.

Abstract

We examine the general issue of whether a scale dependent cosmological constant can be consistent with general covariance, a problem that arises naturally in the treatment of quantum gravitation where coupling constants generally run as a consequence of renormalization group effects. The issue is approached from several points of view, which include the manifestly covariant functional integral formulation, covariant continuum perturbation theory about two dimensions, the lattice formulation of gravity, and the non-local effective action and effective field equation methods. In all cases we find that the cosmological constant cannot run with scale, unless general covariance is explicitly broken by the regularization procedure. Our results are expected to have some bearing on current quantum gravity calculations, but more generally should apply to phenomenological approaches to the cosmological vacuum energy problem.