In the context of loop quantum cosmology, we parametrise the lattice refinement by a parameter, $A$, and the matter Hamiltonian by a parameter, $delta$. 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, $(A,delta)$, parameter space, thereby restricting the types of matter content that can be supported by a particular lattice refinement model.
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