ASHTEKAR VARIABLES, THE THETA-TERM, AND THE COSMOLOGICAL CONSTANT

Capovilla, Jacobson and Dell have given a lagrangian for pure gravity in which only an SO(3) connection and a Lagrange multiplier appears. We show that the introduction of a cosmological constant leads to a non-polynomial action, which we determine to tenth order in the curvature. We point out that, in Ashtekar's hamiltonian formulation, the cosmological constant can be introduced by a transformation that is formally similar to the transformation which leads to a θ-term. © 1990.