The cosmological constant as a boundary term

Abstract

We compare the path integral for transition functions in unimodular gravity and in general relativity. In unimodular gravity the cosmological constant is a property of states that are specified at the boundaries whereas in general relativity the cosmological constant is a parameter of the action. Unimodular gravity with a nondynamical background spacetime volume element has a time variable that is canonically conjugate to the cosmological constant. Wave functions depend on time and satisfy a Schrödinger equation. On the contrary, in the covariant version of unimodular gravity with a 3-form gauge field, proposed by Henneaux and Teitelboim, wave functions are time independent and satisfy a Wheeler-DeWitt equation, as in general relativity. The 3-form gauge field integrated over spacelike hypersurfaces becomes a "cosmic time" only in the semiclassical approximation. In unimodular gravity the smallness of the observed cosmological constant has to be explained as a property of the initial state.

22 pages, minor corrections, agrees with published version

References in corpus (7)

• Cosmology and the Fate of Dilatation Symmetry
• Scale invariance, unimodular gravity and dark energy
• On the UV structure of quantum unimodular gravity
• The path integral of unimodular gravity
• Losing the trace to find dynamical Newton or Planck constants
• Covariant BRST Quantization of Unimodular Gravity I -- Formulation with antisymmetric tensor ghosts --
• Fifth forces and broken scale symmetries in the Jordan frame

Cited by in corpus (2)

• A Quantum-Mechanical Mechanism for Reducing the Cosmological Constant
• Unimodular gravity and the gauge/gravity duality