Inconsistencies from a Running Cosmological Constant

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.

34 pages. Typos fixed, references added, one section expanded

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• Scaling Exponents for Lattice Quantum Gravity in Four Dimensions
• Asymptotic safety and the cosmological constant
• Graviton-Mediated Scattering Amplitudes from the Quantum Effective Action
• Vacuum Condensate Picture of Quantum Gravity
• Cosmological Constant Problem and Renormalized Vacuum Energy Density in Curved Background
• Gravitational Fluctuations as an Alternative to Inflation
• Cosmic eggs to relax the cosmological constant
• Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum
• Quantum and higher curvature corrections to the anti-de Sitter black hole