Bimetric gravitation theory on a cosmological basis

Physics

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Astronomical Models, Cosmology, Field Theory (Physics), Gravitation Theory, Relativity, Universe, Curvature, Mach Inertia Principle, Space-Time Functions

Scientific paper

The background metric tensor in the bimetric theory of gravitation is chosen on the basis of cosmological considerations as the metric tensor of a universe for which the perfect cosmological solution holds; i.e., a spacetime of constant curvature. It is shown that there are three possible forms, corresponding to spatial curvatures given by k = 0, 1, -1. By writing the field equations for an isotropic cosmological model in each of these cases, it is found that only for k = 1 (a closed universe) is it possible to have a model that does not pass through a singular state; this is taken as the appropriate choice for a model of the universe. An approximate solution to the field equations for the present time is constructed which, with suitably chosen values of the parameters, gives agreement with cosmological observations. It is noted that in the case where k = 1, solutions exist which describe models of infinite age that contract from t = negative infinity to t = zero and then expand to t = infinity without going through a singular state.

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