Newtonian cosmology with a time-varying constant of gravitation

Details Newtonian cosmology with a time-varying constant of gravitation Newtonian cosmology with a time-varying constant of gravitation

Jun 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978mnras.183..749m&link_type=abstract

Monthly Notices of the Royal Astronomical Society, vol. 183, June 1978, p. 749-764.

Astronomy and Astrophysics

Astronomy

4

Cosmology, Gravitational Constant, Newton Theory, Time Dependence, Astronomical Models, Euler Equations Of Motion, Flow Equations, Fluid Mechanics, Poisson Equation

Scientific paper

Newtonian cosmology is based on the Eulerian equations of fluid mechanics combined with Poisson's equation modified by the introduction of a time-varying G. Spherically symmetric model universes are worked out with instantaneously uniform densities. They are indeterminate unless instantaneous uniformity of the pressure is imposed. When G varies as an inverse power of the time, the models can in some cases be shown to depend on the solution of a second-order differential equation, which also occurs in the Friedmann models of general relativity. A method for 'passing through' a singularity of this equation is proposed which entails making four arbitrary mathematical assumptions. When G varies as the inverse of time, models with initially cycloidal motion are possible, each cycle becoming longer as time progresses. Finally, gravitation becomes so weak that the model expands to infinity. Kinetic and potential energies for the whole model are derived from the basic equations; their sum is not constant, contrary to the assumption of Landsberg and Bishop (1976) in their treatment of the problem.

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