The reason peculiar velocities grow faster in general relativity than in Newtonian gravity

¹ Departamento de Física, Universidad de Santiago de Chile, Avenida Víctor Jara 3493 Estación Central, 9170124, Santiago, Chile
² Section of Astrophysics, Astronomy and Mechanics, Department of Physics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
³ Clare Hall, University of Cambridge, Herschel Road, Cambridge CB3 9AL, UK

^★ Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 26 January 2026
Accepted: 5 March 2026

Abstract

Context. We provide a theoretical comparison between the Newtonian and quasi-Newtonian studies and the general relativistic analysis of linear cosmological peculiar velocities, in view of the increasing number of surveys reporting bulk peculiar flows much faster and considerably deeper than typically expected.

Aims. We look for a theoretical answer to the ongoing bulk-flow question to explain the fast and deep bulk peculiar motions reported by many recent surveys. These reports have come to be treated as a potentially serious problem for the Lambda cold dark matter (ΛCDM) model since they claim peculiar velocities well in excess of those permitted by the current cosmological paradigm.

Methods. We studied the growth of linear peculiar velocities by employing a general relativistic cosmological perturbations theory and then compared our analytical results with those adopted by the ΛCDM paradigm, which are Newtonian in nature. We did so by means of a unified analysis that facilitates the direct and unambiguous comparison between the Newtonian and the relativistic approaches. This allowed us to identify the differences between the two approaches and to unravel the physical precesses responsible for them.

Results. Our analysis demonstrates that general relativity leads to a linear growth rate of v ∝ t, at a minimum, for the peculiar-velocity field (v) during the Einstein-de Sitter epoch of the universe, namely between recombination and the onset of the recent phase of accelerated expansion. The Newtonian and quasi-Newtonian studies, on the other hand, have led to the substantially weaker growth rate of v ∝ t^1/3 during the same period. The reason behind the difference is that the relativistic analysis also accounts for the gravitational input of the ‘peculiar flux’, that is of the momentum density triggered by the peculiar motion of the matter. We recall that peculiar flows are nothing but matter in motion and that moving matter means non-zero energy flux. We also recall that in general relativity, as opposed to Newtonian gravity, energy fluxes gravitate because they too contribute to the energy-momentum tensor of the matter fields. We show that this extra input of the peculiar flux drastically modifies the driving force of the peculiar-velocity field and, in so doing, it increases the linear velocity growth well beyond the current (Newtonian-based) ΛCDM expectations.

Conclusions. We show that general relativity supports substantially stronger growth rates for the linear peculiar velocities compared to the Newtonian and quasi-Newtonian studies, which in turn leads to faster and deeper residual bulk peculiar flows today. Therefore, one could solve the ongoing bulk-flow puzzle without breaking away from the general framework of the ΛCDM paradigm by simply employing Einstein’s theory instead of Newtonian gravity.