Consistency of canonical quantization of gravity and boundary conditions for the wave function of the Universe

By using the expression given by Halliwell and Hawking, we discuss consistency of the constraint equations of the superspace-quantized gravity coupled to the minimal massive scalar field, in the lowest nontrivial order in the cosmological perturbation. We show that the consistency imposes highly nontrivial conditions on the behavior of the physical state (the wave function of the Universe) at a (the cosmic scale factor) =0.