A Zero-Parameter Extension of General Relativity with Varying Cosmological Constant

Abstract

We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological constant to have a consistent space-time variation, through coding its dynamics in the torsion tensor. We demonstrate this mechanism by adding a `quasi-topological' term to the Einstein action, which naturally realizes a dynamical torsion with an automatic satisfaction of the Bianchi identities. Moreover, variation of the action with respect to this dynamical $\Lambda$ fixes it in terms of other variables, thus providing a scenario with less freedom than general relativity with a cosmological constant. Once matter is introduced, at least in the homogeneous and isotropic reduction, $\Lambda$ is uniquely determined by the field content of the model. We make an explicit construction using the Palatini formulation of GR and describe the striking properties of this new theory. We also highlight some possible extensions to the theory. A companion paper [1] explores the Friedmann--Robertson--Walker reduction for cosmology, and future work will study Solar System tests of the theory.

Companion paper to arXiv:1905.10382. Minor updates to match published version

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Cited by in corpus (19)

• Testing Late Time Cosmic Acceleration with uncorrelated Baryon Acoustic Oscillations dataset
• The cosmology of minimal varying Lambda theories
• Cosmological time and the constants of nature
• Losing the trace to find dynamical Newton or Planck constants
• Limitations on Standard Sirens tests of gravity from screening
• Luminal Propagation of Gravitational Waves in Scalar-tensor Theories: The Case for Torsion
• The real Chern-Simons wave function
• A contextual Planck parameter and the classical limit in quantum cosmology
• A generalized Hartle-Hawking wavefunction
• Quantum cosmology of a dynamical Lambda
• Gravity waves in parity-violating Copernican Universes
• Quantum torsion and a Hartle-Hawking "beam''
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity
• Torsion and the Probability of Inflation
• Canonical structure of minimal varying $\Lambda$ theories
• The Cosmological Constant from Conformal Transformations: Möbius Invariance and Schwarzian Action
• Linking the Baum-Hawking-Coleman Mechanism with Unimodular Gravity and Vilenkin's Probability Flux
• Cosmological Consequences of Varying Couplings in Gravity Action
• Comments on the symmetry breaking condition in MacDowell-Mansouri action