STABILITY BORDERS AND CLASSIFICATION OF DENSITY PERTURBATION PROPAGATIONS IN DEDONDER-GAUGE ON A COSMOLOGICAL BACKGROUND

We investigate the propagation and the stability borders of density an d metric perturbations on a cosmological background in linear perturba tion theory in deDonder-gauge. We obtain the algebraic equations for t he generally time-dependent stability borders by setting the typical t ime for perturbation contrasts infinite in the set of differential equ ations, while all other typical times stay finite. In dD-gauge there a re in general three stability borders whereas in synchronous gauge the re is only one. In the limiting cases of radiation perturbations and ' 'dustlike'' perturbations we obtain in deDonder-gauge no stability bor der resp. only one stability border (the ordinary Jeans limit). The fi rst case is in contrast to the synchronous gauge and means that radiat ion perturbations cannot become unstable. During the recombination the re could be three stability borders. We classify the propagation solut ions and the systems of differential equations governing them by compa ring the characteristic times in the original general system of differ ential equations, in deDonder-gauge and synchronous gauge. The greates t differences for the propagation of density contrasts arise from the presence of a gravitational wave time scale in deDonder-gauge. This be comes significant if the density perturbations are relativistic with r espect to the velocity of sound. Gravitational retardation effects are the origin of the 6-dimensionality of the solution space for density contrasts. This reflects the necessity and physical meaning of gauge s olutions.