Geodesic
Quantum cosmology of multifield scalar matter: Some exact solutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 3, pp. 380-391

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We consider gravity interacting with matter scalar fields and quantized in the superspace approach in which the wave functional is described by the Wheeler–DeWitt equations. Assuming the dominance of the homogeneous and isotropic geometry, we investigate the leading contribution to the wave functional in the minisuperspace approximation with the Friedmann–Robertson–Walker metric and scalar fields depending on the time parameter. We construct a model of several scalar fields with exponential potentials and kinetic terms admitting a special mixing such that it is ultimately possible to separate the variables in the Wheeler–DeWitt equation and find its exact solution in terms of special functions. We study the semiclassical approximation in detail and choose boundary conditions that allow selecting the physical solution for classical cosmologies.
Keywords: quantum cosmology, Wheeler–DeWitt equation, minisuperspace, exponential potential. 
@article{TMF_2015_184_3_a2,
     author = {A. A. Andrianov and O. O. Novikov and Chen Lan},
     title = {Quantum cosmology of multifield scalar matter: {Some} exact solutions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {380--391},
     publisher = {mathdoc},
     volume = {184},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_184_3_a2/}
}
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A. A. Andrianov; O. O. Novikov; Chen Lan. Quantum cosmology of multifield scalar matter: Some exact solutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 3, pp. 380-391. http://geodesic.mathdoc.fr/item/TMF_2015_184_3_a2/