https://doi.org/10.1140/epjc/s10052-025-13777-y
Regular Article - Theoretical Physics
Local peculiar motions in McVittie and LTB spacetimes
1
Department of Physics, Sharif University of Technology, 11155-9161, Tehran, Iran
2
Research Center for High Energy Physics, Department of Physics, Sharif University of Technology, 11155-9161, Tehran, Iran
3
School of Astronomy, Institute for Research in Fundamental Sciences (IPM), 19395-5531, Tehran, Iran
4
Department of Physics and Astronomy, University of Missouri, 65211, Columbia, MO, USA
Received:
10
October
2024
Accepted:
1
January
2025
Published online:
21
January
2025
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.
© The Author(s) 2025
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