Evolution of Scale-invariant Inhomogeneities in Standard Cosmology

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It is shown that density fluctuations obey a scaling law in an open Friedmann universe. In a flat universe, the fluctuations are not scale-invariant. We compute the growth rate of adiabatic scale-invariant density fluctuations in flat, open and inflationary universes. We find that, given a sufficiently long time, the density perturbations decay away in the Einstein-de-Sitter universe. On the contrary, the rapid growth of the density instabilities makes an open universe inhomogeneous in a time scale comparable to the age of our universe. We also find that the fluctuations grow exponentially in a flat inflationary universe.