Geodesic
Quantum gravitation: Quantization of the Friedmann model
Teoretičeskaâ i matematičeskaâ fizika, Tome 33 (1977) no. 3, pp. 364-376

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Cosmological model of the Friedmann world filled by ideal liquid with the equation of state $p=K\rho$ is studied in the framework of explicit canonical quantization of gravitation by the Arnowitt–Deser–Misner (ADM) method and in the framework of the superspatial Dirac method. It is shown that the collapse does not take place in the model (the Dirac method and the ADM method when the time is chosen out of matter variables). If the time is chosen out of geometrical variables, the Friedmann Universe can be in the eigen-state of the Hamiltonian with the energy eigen-values depending on time. Physical interpretation of the results obtained is discussed. 
@article{TMF_1977_33_3_a6,
     author = {V. G. Lapchinskii and V. A. Rubakov},
     title = {Quantum gravitation: {Quantization} of the {Friedmann} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {364--376},
     publisher = {mathdoc},
     volume = {33},
     number = {3},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1977_33_3_a6/}
}
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V. G. Lapchinskii; V. A. Rubakov. Quantum gravitation: Quantization of the Friedmann model. Teoretičeskaâ i matematičeskaâ fizika, Tome 33 (1977) no. 3, pp. 364-376. http://geodesic.mathdoc.fr/item/TMF_1977_33_3_a6/