Mathematics
Scientific paper
Aug 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983jpha...16.2757b&link_type=abstract
Journal of Physics A - Mathematical and General (ISSN 0305-4470), vol. 16, Aug. 21, 1983, p. 2757-2776.
Mathematics
274
Cosmology, Einstein Equations, Numerical Stability, Relativity, Space-Time Functions, Astronomical Models, Field Theory (Physics), Formalism, Gravitational Fields, Singularity (Mathematics)
Scientific paper
The behavior of homogeneous and isotropic solutions to the gravity theory that arises from the variation of an arbitrary analytic function of the scalar curvature of space-time is analyzed. An existence theorem needed for the de Sitter cosmological solution of general relativity (GR) to exist as a solution of the general function of scalar curvature f(R) in the Lagrangian theory of gravity is proved and the stability properties of any de Sitter solution that does exist is examined. The existence and stability of the Friedmann solutions of GR in f(R) theories are studied,and the asymptotic behavior of these Friedmann solutions for both large and small cosmic times is investigated. The conditions on the function necessary for an initial big bang singularity are derived. The existence and stability of Einstein's static universe and flat Minkowski space are examined and the conditions for the stability of Minkowski space are related to the behavior of cosmological models in f(R) theories.
Barrow John D.
Ottewill Adrian C.
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