Quasi-linear regime of gravitational instability as a clue to understanding the large-scale structure in the Universe

In the late seventies, an image of the large-scale structure in the Universe began to emerge as a result of the accumulation of the galaxy redshifts. Most of the galaxies are found to concentrate in large filaments and perhaps sheets leaving most of the volume empty. Similar structures were predicted theoretically in the frame of the adiabatic theory of galaxy formation (Zeldovich) and later in the hot dark matter cosmology. However, both scenarios have been ruled out by the observations. With these scenarios the dynamical part of the scenario was also erroneously rejected by many as well. In this talk, I derive the Zeldovich approximation from the exact dynamic equations and show that it is always better than the standard linear approximation. The advantage of the Zeldovich approximation is the greatest in the quasi-linear regime when delta(sub rms) is less than 1 (delta identical to delta(rho)/rho), but the displacement of the matter is essential. The range of scales in the quasi-linear regime depends upon the slope of the initial spectrum and increases with decreasing n, where n is the exponent, if the initial spectrum is approximated by a simple power law P(k) varies as k(exp n).