On deformations of Ashtekar's constraint algebra

Abstract

We show that the constraint algebra of Ashtekar's Hamiltonian formulation of general relativity can be non-trivially deformed by allowing the cosmological constant to become an arbitrary function of the (Weyl) curvature. Our result implies that there is not one but infinitely many (parameterized by an arbitrary function) four-dimensional gravity theories propagating two degrees of freedom.

3 pages, no figures

References in corpus (4)

• Bouncing Universes in String-inspired Gravity
• Non-Metric Gravity I: Field Equations
• Note on non-metric gravity
• Non-Metric Gravity II: Spherically Symmetric Solution, Missing Mass and Redshifts of Quasars

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