Lattice refining loop quantum cosmology and the matter Hamiltonian

In the context of loop quantum cosmology, we parametrize the lattice refinement by a parameter, A, and the matter Hamiltonian by a parameter, δ. We then solve the Hamiltonian constraint for both a self-adjoint and a non-self-adjoint Hamiltonian operator. Demanding that the solutions for the wave functions obey certain physical restrictions, we impose constraints on the two-dimensional, (A,δ), parameter space, thereby restricting the types of matter content that can be supported by a particular lattice refinement model.