Abstract
Given that observations seem to favour a density parameter Ω0<1, corresponding to an open universe, we consider gauge-invariant perturbations of nonflat Robertson-Walker universes filled with a general imperfect fluid which can also be taken to represent a scalar field. Our aim is to set up the equations that govern the evolution of the density perturbations Δ so that it can be determined through a first order differential equation with a quantity [Formula: see text] which is conserved at any length scale, even in nonflat universe models, acting as a source term. The quantity [Formula: see text] generalizes other variables that are conserved in specific cases (for example at large scales in a flat universe) and is useful to connect different epochs in the evolution of density perturbations via a transfer function. We show that the problem of finding a conserved [Formula: see text] can be reduced to determining two auxiliary variables X and Y, and illustrate the method with two simple examples.
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