On the Formation of Condensation in an Expanding Universe
Masa-aki Kondo · Publications of the Astronomical Society of Japan · 1969
Abstract Recently, KIHARA derived hydrodynamical equations applicable in homogeneous isotropic expanding universe within the approximation to the first order of smallness with respect to a metric perturbation, including all nonlinear effects of density perturbations, and obtained the particular soltion starting from the background state. In this paper, general solutions with arbitrary initial conditions are obtained analytically for the case in which the disturbance is one-dimensional and the wavelength is much longer than the Jeans wavelength. There are two families of solutions, one of which indicates a maximum-density region of perturbation undergoing free fall while the other indicates the opposite character. The density in the free-fall part becomes infinite within a finite time which is given as a function of initial conditions. There is no essential difference in the characteristics of the density-velocity phase plane between the case of the expanding universe and that of the static Newtonian universe.