Discrete quantum gravity: cosmological examples

We consider the application of the ‘consistent lattice quantum gravity’ approach we introduced recently to the situation of a Friedmann cosmology and also to Bianchi cosmological models. This allows us to work out in detail the computations involved in the determination of the Lagrange multipliers that impose consistency of the discretized equations, and the implications of this determination. It also allows us to study the removal of the Big Bang singularity. Different discretizations can be achieved depending on the version of the classical theory chosen as a starting point and their relationships studied. We analyse in some detail how the continuum limit arises in various models. In particular, we note how remnants of the symmetries of the continuum theory are embodied in constants of the motion of the consistent discrete theory. The unconstrained nature of the discrete theory allows the consistent introduction of a relational time in quantum cosmology, free from the usual conceptual problems. The examples show that in simple settings the proposal works satisfactorily.