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