Normal Modes of Vibrations of the Universe

This paper reviews some aspects of our knowledge of the gravitational theory of fluctuations of density in homogeneous and isotropic models of the universe. Irrotational fluid motions only are considered. All perturbations are assumed to be small and a normal mode analysis is used. The nature and time dependence of the amplitude of the various modes in expanding and contracting models of the universe are considered within the framework of Newtonian and general relativity theories. The origin of celestial structure requires that a uniform universe is unstable against arbitrarily small perturbations. However, the rate of growth of the allowed modes, particularly in an expanding universe, is sufficiently slow to cast doubt on the instability of the models.