On deformations of Ashtekar's constraint algebra

TL;DR

This paper demonstrates that Ashtekar's constraint algebra in general relativity can be deformed by making the cosmological constant a function of curvature, leading to infinitely many gravity theories with two degrees of freedom.

Contribution

It introduces a novel deformation of the constraint algebra allowing a variable cosmological constant, expanding the landscape of 4D gravity theories.

Findings

Constraint algebra can be non-trivially deformed.

Infinite family of gravity theories with two degrees of freedom.

Deformation depends on an arbitrary function of curvature.

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.