Mathematics
Scientific paper
May 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977afz....13..345r&link_type=abstract
Astrofizika, vol. 13, May 1977, p. 345-360. In Russian.
Mathematics
9
Anisotropy, Cosmology, Gravitation Theory, Quantum Theory, Relativity, Astronomical Models, Invariance, Numerical Integration, Singularity (Mathematics)
Scientific paper
It is noted that quantum modifications of the general-relativistic equations near the cosmological singularity can be partially achieved by adding terms in the square of the curvature tensor to the Lagrangian of the gravitational field. Such a modified theory is found to yield solutions with a regular minimum at t = 0 in the general anisotropic case. However, analysis of the simplest homogeneous and anisotropic metric indicates that these solutions are not characterized by power-law asymptotic behavior as t tends to infinity. It is shown that allowance for certain logarithmic terms in the curvature tensor alters the situation slightly, at least in the isotropic case. It is concluded that effects of particle production and possibly of nonlocal terms must be taken into account in a self-consistent manner in order to resolve the question of whether the cosmological singularity can be eliminated by a transformation to power-law behavior.
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