Peculiar velocities in Friedmann universes with nonzero spatial curvature

TL;DR

This paper extends the analysis of cosmological peculiar velocities to Friedmann universes with nonzero spatial curvature, revealing that curvature influences the growth rates of peculiar velocities and confirming stronger relativistic effects compared to Newtonian models.

Contribution

It provides relativistic differential equations for peculiar velocities in curved Friedmann universes and compares their growth rates across different spatial curvatures, extending previous flat universe studies.

Findings

Relativistic analysis shows stronger growth rates than Newtonian models.

Positive curvature leads to faster peculiar velocity growth.

Open universes exhibit slower growth of peculiar velocities.

Abstract

We extend the earlier linear studies of cosmological peculiar velocities to Friedmann universes with nonzero spatial curvature. In the process, we also compare our results with those obtained in cosmologies with Euclidean spatial sections. Employing relativistic cosmological perturbation theory, we first provide the differential formulae governing the evolution of peculiar velocities on all Friedmann backgrounds. The technical complexities of the curved models, however, mean that analytic solutions are possible only in special, though characteristic, moments in the lifetime of these universes. Nevertheless, our solutions exhibit persistent patterns that make us confident enough to generalise them. Thus, we confirm earlier claims that, compared to the Newtonian studies, the relativistic analysis supports considerably stronger linear growth-rates for peculiar-velocity perturbations. This result holds irrespective of the background curvature. Moreover, for positive curvature, the peculiar growth-rate is found to be faster than that obtained in a spatially flat Friedman universe. In contrast, linear peculiar velocities appear to grow at a slower pace when their Friedmann host is spatially open. Extrapolating them to the present, our results seem to suggest faster bulk peculiar motions in overdense, rather than in underdense, regions of the universe.