INHOMOGENEITY OF COLD DARK-MATTER DUE TO INITIAL FLUCTUATIONS IN THE LONG COSMIC-STRING SCHEME .1.

It is investigated numerically how the inhomogeneity of dark matter pr oceeds in the long cosmic string model of galaxy formation. Wakes havi ng sheetlike structures are naturally formed in this model; however, t he appropriate fluctuations of dark matter are necessary for the devel opment of inhomogeneity in them, which grows up into astronomical obje cts such as galaxies. The growth of inhomogeneity of dark matter is ca lculated for two types of initial fluctuations, such as the standard c old dark matter fluctuations and a Gaussian flat spectrum (n = 0). If the amplitude of the fluctuations is too large, even the wakes are not formed, and if too small, astronomical objects are not formed within a wake. Typical isodensity surfaces in some representative cases are p resented, and we have derived the suitable amplitude range of initial fluctuations for each spectrum type, taking into account the condition s for wake formation and galaxy formation in wakes, which is relativel y limited.