Was Entropy Conserved between BBN and Recombination?*

The production of entropy after big bang nucleosynthesis (BBN) is a popular extension to the

standard ΛCDM cosmology due to its ability to alter the expansion history of the Universe and

possibly alleviate the Hubble tension. We establish new bounds on entropy injection between BBN

and recombination by considering a generic massive particle that decays into a mixture of photons

and/or other relativistic species (e.g. dark radiation). The injection of new relativistic particles

after neutrino decoupling generally causes a change to the effective number of neutrinos, N_eff,

which is strongly constrained by observations of small-scale anisotropies in the cosmic microwave

background (CMB). Since CMB anisotropies tightly constrain the baryon density, measurements of

the abundances of light elements strictly limit the injection of new photons, even if they do not have

sufficient energy to photo-disintegrate light nuclei. We combine the constraining power of CMB

anisotropies, deuterium abundance measurements, and the CMB spectrum to derive bounds on the

amount and type of radiation that can be injected by a decaying particle. If the injected particles

consist of a mixture of photons and dark radiation that does not considerably alter N_eff, Planck

data alone allows for significant entropy injection after neutrino decoupling. However, bounds on

the primordial deuterium abundance severely limit any injections of new photons after BBN.