Quantum cosmology of a dynamical Lambda

By allowing torsion into the gravitational dynamics one can promote the cosmological constant Lambda to a dynamical variable in a class of quasitopological theories. In this paper we perform a minisuperspace quantization of these theories in the connection representation. If Lambda is kept fixed, the solution is a delta-normalizable version of the Chern-Simons (CS) state, which is the dual of the Hartle and Hawking and Vilenkin wave functions. We find that the CS state solves the Wheeler-De Witt equation also if Lambda is rendered dynamical by an Euler quasitopological invariant, in the parity-even branch of the theory. In the absence of an infrared (IR) cutoff, the CS state suggests the marginal probability P(Lambda) = delta(Lambda). Should there be an IR cutoff (for whatever reason), the probability is sharply peaked at the cut off. In the parity-odd branch, however, we can still find the CS state as a particular (but not most general) solution, but further work is needed to sharpen the predictions. For the theory based on the Pontryagin invariant (which only has a parity-odd branch) the CS wave function no longer is a solution to the constraints. We find the most general solution in this case, which again leaves room for a range of predictions for Lambda.