General relativistic analysis of peculiar velocities

TL;DR

This paper provides a detailed general relativistic framework for analyzing cosmological peculiar velocities caused by matter density fluctuations, extending Newtonian results to a relativistic context.

Contribution

It introduces a (1+3)-covariant approach to relate peculiar velocities and accelerations in a relativistic setting, including new generalized equations.

Findings

Derived relativistic generalizations of Newtonian velocity-acceleration relations.

Identified conditions for alignment of peculiar velocity and acceleration.

Established a covariant framework for peculiar velocity analysis in cosmology.

Abstract

We give a careful general relativistic and (1+3)-covariant analysis of cosmological peculiar velocities induced by matter density perturbations in the presence of a cosmological constant. In our quasi-Newtonian approach, constraint equations arise to maintain zero shear of the non-comoving fundamental worldlines which define a Newtonian-like frame, and these lead to the (1+3)-covariant dynamical equations, including a generalized Poisson-type equation. We investigate the relation between peculiar velocity and peculiar acceleration, finding the conditions under which they are aligned. In this case we find (1+3)-covariant relativistic generalizations of well-known Newtonian results.