Generic Peculiar Motions in FLRW Spacetimes

TL;DR

This paper analyzes the effects of peculiar motions in FLRW spacetimes by constructing Fermi normal coordinates around a boosted mass and examining the resulting gravitomagnetic fields.

Contribution

It introduces a method to compare local metrics around boosted and comoving observers in FLRW spacetimes, highlighting peculiar motion effects.

Findings

Construction of Fermi normal coordinates around a boosted mass

Comparison of metrics between boosted and comoving observers

Identification of gravitomagnetic fields due to peculiar motions

Abstract

In the standard Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime, we consider a local cosmic test mass that is boosted in some direction relative to the standard comoving observers. The geodesic (Fermi) normal coordinate system established around the world line of the boosted cosmic mass is constructed within an approximation scheme and the resulting spacetime metric is compared with the corresponding metric of the Fermi system established around the world line of a comoving observer. The circular gravitomagnetic field around the direction of motion of the boosted cosmic mass is studied.