Local Peculiar Motions in McVittie and LTB Spacetimes

TL;DR

This paper investigates local peculiar motions of test particles in inhomogeneous cosmological models, specifically McVittie and LTB spacetimes, analyzing tidal effects and comparing their behaviors within these models.

Contribution

It provides an invariant characterization of peculiar motions in McVittie and LTB spacetimes using Fermi normal coordinates, highlighting differences in tidal dynamics.

Findings

Peculiar motions are influenced by inhomogeneity and background curvature.

Tidal dynamics in McVittie involves multiple curvature contributions.

LTB model's tidal behavior resembles Einstein-de Sitter universe.

Abstract

We consider two inhomogeneous cosmological models, namely, the flat McVittie spacetime and a simple specific LTB spacetime. Relative to the world line of a reference comoving observer that remains spatially at rest, we study the local deviations of the world lines of free test particles. These local peculiar motions can be invariantly characterized within the framework of a quasi-inertial Fermi normal coordinate system established along the world line of the reference comoving observer. Tidal dynamics in the McVittie model involves the sum of the curvature due to the inhomogeneity, the curvature due to the background FLRW spacetime and a mixed term, while tidal dynamics in the particular LTB model turns out to be qualitatively the same as in the Einstein-de Sitter universe. Peculiar motions in the two cosmological models are briefly compared and contrasted.