P, T AND THE COSMOLOGICAL CONSTANT

Parity inversion P and time reversal T are studied, in a coordinate dependent way, for Einstein’s theory of gravity written in terms of spatial triads. We point out that the content of these operations may be changed by field redefinitions that change the tensor density weight of the triad. We define new operations P and T, having no counterpart for conventional weight assignments, which transform the Lagrangian density in the expected way if and only if the cosmological constant is zero. However, important matter couplings also “misbehave” under these new operations. We are unable to show that the “old” operations P and T leave the action invariant, if one uses Ashtekar’s variables, and extends the phase space to include degenerate triads.