Covariance in self dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems

Understand

When applying the techniques of Loop Quantum Gravity (LQG) to symmetry-reduced gravitational systems, one first regularizes the scalar constraint using holonomy corrections, prior to quantization.

• In inhomogeneous system, where a residual spatial diffeomorphism symmetry survives, such modification of the gauge generator generating time reparametrization can potentially lead to deformations or anomalies in the modified algebra of first class constraints.
• When working with self-dual variables, it has already been shown that, for spherically symmetric geometry coupled to a scalar field, the holonomy-modified constraints do not generate any modifications to general covariance, as one faces in the real variables formula- tion, and can thus accommodate local degrees of freedom in such inhomogeneous models.
• In this paper, we extend this result to Gowdy cosmologies in the self-dual Ashtekar formulation.