Abstract
By allowing torsion into the gravitational dynamics one can promote the cosmological constant 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 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 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 . 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 .
- Received 19 June 2020
- Accepted 20 August 2020
DOI:https://doi.org/10.1103/PhysRevD.102.064006
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