ROTATION CURVES OF SPIRAL GALAXIES AND LARGE-SCALE STRUCTURE OF THE UNIVERSE UNDER GENERALIZED EINSTEIN ACTION

Abstract

We consider an addition of the term which is a square of the scalar curvature to the Einstein-Hilbert action. Under this generalized action, we attempt to explain (i) the flat rotation curves observed in spiral galaxies, which is usually attributed to the existence of dark matter, and (ii) the contradicting observations of the uniform cosmic microwave background and the nonuniform galaxy distributions against redshift. For the former, we attain the flatness of velocities, although the magnitudes remain about half that of the observations. For the latter, we obtain a solution with the oscillating Hubble parameter under uniform mass distributions. This solution leads to several peaks of galaxy number counts as a function of redshift with the first peak corresponding to the Great Wall.