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We consider an addition of the term which is a square of the scalar curvatureto the Einstein-Hilbert action. Under this generalized action, we attempt toexplain i) the flat rotation curves observed in spiral galaxies, which isusually attributed to the existence of dark matter, and ii) the contradictingobservations of uniform cosmic microwave background and non-uniform galaxydistributions against redshift. For the former, we attain the flatness ofvelocities, although the magnitudes remain about half of the observations. Forthe latter, we obtain a solution with oscillating Hubble parameter underuniform mass distributions. This solution leads to several peaks of galaxynumber counts as a function of redshift with the first peak corresponding tothe Great Wall.Comment: 16 page

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