General gravitational Lagrangian with deformed covariance

We derive the gravitational Lagrangian to all orders of curvature when the canonical constraint algebra is deformed by a phase space function as predicted by some studies into loop quantum cosmology. The deformation function seems to be required to satisfy a nonlinear conservation equation usually found in fluid mechanics and can form discontinuities quite generally. These results arise from attempting to consistently incorporate general spatial inhomogeneities in effective models of loop quantum cosmology rather than directly investigating the nature of signature change in such models. We work within the restriction of not allowing additional degrees of freedom.