Dust reference frame in quantum cosmology

give a formulation of quantum cosmology with pressureless dust and arbitrary additional matter fields. The system has the property that its Hamiltonian constraint is linear in the dust momentum. This feature provides a natural time gauge, leading to a physical Hamiltonian that is not a square root. Quantization leads to a Schrodinger equation for which unitary evolution is directly linked to geodesic completeness. Our approach simplifies the analysis of both Wheeler-deWitt and loop quantum cosmology (LQC) models and significantly broadens the applicability of the latter. This is demonstrated for arbitrary scalar field potential and cosmological constant in LQC.