The Effective Theory of Gravity and Dynamical Vacuum Energy

Abstract

Gravity and general relativity are considered as an Effective Field Theory at low energies and macroscopic distances. The effective action of the conformal anomaly of light or massless quantum fields has significant effects on macroscopic scales, due to associated light cone singularities that are not captured by an expansion in local curvature invariants. A compact local form for the WZ effective action of the conformal anomaly and stress tensor is given, requiring the introduction of a new light scalar field, which it is argued should be included in the low energy effective action for gravity. The scalar conformalon couples to the conformal part of the spacetime metric and allows the effective value of the vacuum energy, described as a condensate of a 4-form abelian gauge field strength F=dA, to change in space and time. This is achieved by the identification of the torsion dependent part of the Chern-Simons 3-form of the Euler class with the gauge potential A, which enters the effective action of the conformal anomaly as a J.A interaction analogous to electromagnetism. The conserved 3-current J describes the worldtube of 2-surfaces that separate regions of differing vacuum energy. The resulting EFT thus replaces the fixed constant Lambda of classical gravity, and its apparently unnaturally large sensitivity to UV physics, with a dynamical condensate whose ground state value in empty flat space is Lambda = 0 identically. By allowing Lambda to vary rapidly near the 2-surface of a black hole horizon, the proposed EFT of dynamical vacuum energy provides an effective Lagrangian for gravitational condensate stars, as the final state of complete gravitational collapse consistent with quantum theory. The possible consequences of dynamical vacuum dark energy for cosmology, the cosmic coincidence problem, and the role of conformal invariance for other fine tuning issues in the SM are discussed.

41 pages, Revised Version published in JHEP 2022, 37 (2022). Previous Sec. 2 expanded to Secs. 2-3. The role of the torsional part of the Chern-Simons 3-form and source current for the 4-form field strength clarified in Secs. 5-7. Previous Sec. 5 moved to Appendix B and modified to discuss torsional susceptibility kappa. Previous Sec. 6 eliminated as unnecessary. Conclusions are unchanged

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• Rotating black holes in semiclassical gravity
• Regular Black Holes and Horizonless Ultra-Compact Objects in Lorentz-Violating Gravity
• Notes on conformal anomaly, nonlocal effective action and the metamorphosis of the running scale
• Embedding Unimodular Gravity in String Theory
• Quantum Effects of the Conformal Anomaly in a 2D Model of Gravitational Collapse
• Effective approach to the Antoniadis-Mottola model: quantum decoupling of the higher derivative terms
• Overspinning a rotating black hole in semiclassical gravity with type-A trace anomaly
• Macroscopic backreaction of the trace anomaly on classical vacuum backgrounds
• Trace anomaly contributions to semi-classical wormhole geometries