https://doi.org/10.1140/epjp/s13360-025-07088-0
Regular Article
Apparent proper motions induced by the residual anisotropic expansion of a Bianchi I 
CDM Universe
Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Université Côte d’Azur, Nice, France
Received:
25
September
2025
Accepted:
15
November
2025
Published online:
28
November
2025
The motion of light in a dust-filled weakly Bianchi I Universe is analytically investigated. The anisotropic expansion causes a specific proper motion of comoving sources (an often neglected effect). We provide in this paper this proper motion in terms of usual cosmological parameters and observables. This specific “anisotropic proper motion” is also converted into local velocity, which yields a surprisingly simple expression for cosmological sources, that allows a direct comparison with (true) expected local physical velocities. While the Bianchi I solution depends on two parameters K and 
, it turns out that the amplitude of this anisotropic motion through the whole sky only marginally depends on , ie is essentially mastered by K. Constraining K with the Planck mission data, it is found that this induced local velocity is below the 
range for cosmological sources with 
, which makes the related cosmological and astrometric effects a priori hard to disentangle from local proper motions in the foreseeable future.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
