Consistent discretization of the Gowdy cosmologies

We report joint work with Rodolfo Gambini and Marcelo Ponce in which the consistent discretization scheme (a way of discretizing constrained theories in such a way that the constraints are satisfied, with potentially interesting applications in quantum gravity as well) to the Gowdy cosmologies. This is the first time the formalism is applied to a situation with field-theoretic degrees of freedom. The numerics is quite challenging since the resulting equations are implicit and coupled. We show successful and convergent evolutions for the ``gauge wave'' situation.