Newtonian Hydrodynamics in an Expanding Universe in Terms of the Scalar-Tensor Theory

TLDR: In this paper, a formalism for dealing with various non-linear effects of cosmic fluid being important during the formation of galaxies is developed in comparison with the previous one based on the general relativistic cosmology.

Abstract: In view of a possible relevance of the scalar-tensor theory of gravity to various cosmo­ logical and astrophysical problems, Newtonian hydrodynamics suitable at the matter dominant stage of the Brans-Dicke universe is formulated and a formalism for dealing with various non-linear effects of cosmic fluid being important during the formation of galaxies is devel­ oped in comparison with the previous one based on the general relativistic cosmology. In contrast with the situation in the linear theory of gravitational instability, it is shown in the case of a density perturbation with spherical symmetry that the critical epoch and density ratio for the occurrence of gravitational binding at the center may considerably be different from those in the Friedmann universe. Dynamical equations for a rotating gaseous ellipsoid with uniform density are also derived and their general features are touched upon.