Mixing electromagnetic radiation with dark radiation between BBN and recombination dilutes the baryon-to-entropy ratio, tightening the allowed total extra radiation to at most ~25% more than dark-radiation-only scenarios.
Was entropy conserved between BBN and recom- bination?
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Constraints on the Injection of Radiation in the Early Universe
Mixing electromagnetic radiation with dark radiation between BBN and recombination dilutes the baryon-to-entropy ratio, tightening the allowed total extra radiation to at most ~25% more than dark-radiation-only scenarios.