I will show that the Weyl-Wigner-Groenewold formalism of the cosmological quantum state is described by the Moyal-Wheeler-DeWitt deformation quantization equation with symplectic solutions in the Moyal-Wigner phase space: this is philosophically of foundational importance since quantum gravity necessitates that spacetime is quantized in a way described by the Moyal-Wheeler-DeWitt equation:

where in the deformation quantization Hilbert space formalism, the deformed operator in the scalar product relative to is given by:

with a skew-symmetric matrix on , and , , and the deformation quantization differential operator is given by:

The central property of the cosmological quantum state is that it must entail the emergence of a classical universe satisfying all of the observable properties induced by the Friedmann-Robertson-Walker space-time, where such a FRW-space-time flat line-element, curved by quantum deformation, is:

with curved space-time metric:

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