CONSERVATION-LAWS AND COSMOLOGICAL PERTURBATIONS IN CURVED UNIVERSES

When working in synchronous gauges, pseudo-tenser conservation laws ar e often used to set the initial conditions for cosmological scalar per turbations, when those are generated by topological defects which sudd enly appear in an up to then perfectly homogeneous and isotropic unive rse. However those conservation laws are restricted to spatially flat (K=0) Friedmann-Lemaitre spacetimes. In this paper, we first show that in fact they implement a matching condition between the pre-and post- transition eras and, in doing so, we are able to generalize them and s et the initial conditions for all K. Finally, in the long wavelength l imit, we encode them into a vector conservation law having a well-defi ned geometrical meaning.