Reduced phase space quantization of Ashtekar's gravity on de Sitter background

TL;DR

This paper develops a reduced phase space quantization of Ashtekar's gravity on a de Sitter background, revealing its equivalence to ADM gravity and clarifying gauge fixing procedures for perturbations.

Contribution

It provides a perturbative reduction of constraints and gauge fixing for Ashtekar's gravity on de Sitter space, connecting it to ADM formalism.

Findings

Reduced phase space consists of transverse, traceless fluctuations of triad and connection.

Gauge freedom related to conformal Killing vectors can be partially fixed.

Reduced phase space is equivalent to ADM gravity on de Sitter background.

Abstract

We solve perturbative constraints and eliminate gauge freedom for Ashtekar's gravity on de Sitter background. We show that the reduced phase space consists of transverse, traceless, symmetric fluctuations of the triad and of transverse, traceless, symmetric fluctuations of the connection. A part of gauge freedom corresponding to the conformal Killing vectors of the three-manifold can be fixed only by imposing conditions on Lagrange multiplier. The reduced phase space is equivalent to that of ADM gravity on the same background.