Geodesic
The World Lines of Isotropic Expansion in the De Sitter Universe
Publications of the Department of Astronomy, Tome 12 (1983) no. 1.

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The well-known Lemaitre coordinate transformation in de Sitter's spacetime, leading to an expanding Euclidean spatial metric, is obtained here as a particular case in a family of transformations. These transformations lead to non-geodesic radial world lines (except ,in the Lemaitre case) of isotropic expansion, with determined consequences for the metric and the acceleration of particles on them. 
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     author = {I. Lukav\v{c}evi\'c},
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I. Lukavčević. The World Lines of Isotropic Expansion in the De Sitter Universe. Publications of the Department of Astronomy, Tome 12 (1983) no. 1. http://geodesic.mathdoc.fr/item/PDA_1983_12_1_a2/