Geodesic
The~self-consistent field method and macroscopic Einstein equations for the~early universe
Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 1, pp. 106-129

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Using a self-consistent field, we construct a complete theory of the macroscopic description of cosmological evolution, including a subsystem of linear equations for the evolution of perturbations and nonlinear macroscopic Einstein equations and a scalar field. We present example solutions of this system showing the principal difference between cosmological models of the early universe constructed on homogenous and locally fluctuating scalar fields.
Keywords: macroscopic gravitation, self-consistent field, cosmological model, scalar field, averaging local fluctuations, asymptotic behavior, cosmological singularity. 
@article{TMF_2020_204_1_a6,
     author = {Yu. G. Ignat'ev},
     title = {The~self-consistent field method and macroscopic {Einstein} equations for the~early universe},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {106--129},
     publisher = {mathdoc},
     volume = {204},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_204_1_a6/}
}
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Yu. G. Ignat'ev. The~self-consistent field method and macroscopic Einstein equations for the~early universe. Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 1, pp. 106-129. http://geodesic.mathdoc.fr/item/TMF_2020_204_1_a6/