Some exact solutions to the Friedmann equations with the cosmological constant

Details Some exact solutions to the Friedmann equations with the cosmological constant Some exact solutions to the Friedmann equations with the cosmological constant

Dec 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976azh....53.1145k&link_type=abstract

Astronomicheskii Zhurnal, vol. 53, Nov.-Dec. 1976, p. 1145-1152. In Russian.

Mathematics

Logic

Astronomical Models, Cosmology, Einstein Equations, Relativity, Universe, Cosmic Dust, Elliptic Functions, Isotropic Media, Metric Space

Scientific paper

Some exact solutions to the Friedmann equations with inclusion of the cosmological constant are presented for both dust-filled and radiation-dominated universes. In all cases, the metric is expressed conformally, and the dependence of real time on parametric time is determined for all possible values of the cosmological constant and a scale-factor variable. Solutions are obtained for a cosmological model characterized by a repulsive force, type O2 and M2 models, type A1 and A2 models, and a model characterized by cosmological attractive forces. It is shown that the solutions for type A1 and A2 models are expressed in elementary functions, while those for type O2, M1, and M2 models are expressed in elliptic functions.

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