Peculiar velocities grow proportionally to time in the Einstein-de Sitter era but experience progressive suppression and eventual decay in the Lambda-dominated phase, with residual growth persisting to the present day.
Tsagas, Astrophys
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Peculiar velocities in the $\Lambda$CDM universe
Peculiar velocities grow proportionally to time in the Einstein-de Sitter era but experience progressive suppression and eventual decay in the Lambda-dominated phase, with residual growth persisting to the present day.