CONSERVED QUANTITIES IN PERTURBED INFLATIONARY UNIVERSES

Given that observations seem to favour a density parameter Omega(0) < 1, corresponding to an open universe, we consider gauge-invariant pert urbations of nonflat Robertson-Walker universes filled with a general imperfect fluid which can also be taken to represent a scalar field. O ur aim is to set up the equations that govern the evolution of the den sity perturbations Delta so that it can be determined through a first order differential equation with a quantity kappa which is conserved a t any length scale, even in nonflat universe models, acting as a sourc e term. The quantity kappa generalizes other variables that are conser ved 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 fi nding a conserved kappa can be reduced to determining two auxiliary va riables X and Y, and illustrate the method with two simple examples.