Non-Linear Theory of Gravitational Instability in the Expanding Universe. III

First it is indicated that, at the radiation-dominated stage of the expanding universe, two ways should be distinguished for the evolution of the second-order density waves most naturally associated with the first-order rotational and gravitational waves, and the behavior of an isolated eddy is examined for a comparison with those of periodically distributed eddies. Next the second-order waves associated with rotational, density and their mixed waves at the intermediate stage (before and after the decoupling epoch tD) are analyzed and the rapidity of compression due to the inertial force appearing soon after tD is calculated. Finally the possibility of galaxy formation is examined on the basis of the above analysis. Moreover a possibility for comparatively small galaxies to be formed through the cascade due to non-linear process is considered.