  Loop quantum cosmology, the symmetry reduction of quantum geometry for the
study of various cosmological situations, leads to a difference equation for
its quantum evolution equation. To ensure that solutions of this equation act
in the expected classical manner far from singularities, additional
restrictions are imposed on the solution. In this paper, we consider the
Bianchi I model, both the vacuum case and the addition of a cosmological
constant, and show using generating function techniques that only the zero
solution satisfies these constraints. This implies either that there are
technical difficulties with the current method of quantizing the evolution
equation, or else loop quantum gravity imposes strong restrictions on the
physically allowed solutions.
