  We show how, in canonical quantum cosmology, the frame fixing induces a new
energy density contribution having features compatible with the (actual) cold
dark matter component of the Universe. First we quantize the closed
Friedmann-Robertson-Walker (FRW) model in a sinchronous reference and determine
the spectrum of the super-Hamiltonian in the presence of ultra-relativistic
matter and a perfect gas contribution. Then we include in this model small
inhomogeneous (spherical) perturbations in the spirit of the Lemaitre-Tolman
cosmology. The main issue of our analysis consists in outlining that, in the
classical limit, the non-zero eigenvalue of the super-Hamiltonian can make
account for the present value of the dark matter critical parameter.
Furthermore we obtain a direct correlation between the inhomogeneities in our
dark matter candidate and those one appearing in the ultra-relativistic matter.
