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We consider the 21cm absorption signal expected at high redshift incosmologies with and without non-baryonic cold dark matter. The expansion ofthe early universe decelerates strongly with dark matter, but approximatelycoasts without it. This results in a different path length across the epochswhen absorption is expected, with the consequence that the absorption ispredicted to be a factor of $\sim 2$ greater without dark matter than with it.Observation of such a signal would motivate consideration of extended theoriesof gravity in lieu of dark matter.

Predictions for the sky-averaged depth of the 21cm absorption signal at high redshift in cosmologies with and without non-baryonic cold dark matter