Dark Radiation from Particle Decays during Big Bang Nucleosynthesis

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Cosmic microwave background (CMB) observations suggest the possibility of an extra dark radiation component, while the current evidence from big bang nucleosynthesis (BBN) is more ambiguous. Dark radiation from a decaying particle can affect these two processes differently. Early decays add an additional radiation component to both the CMB and BBN, while late decays can alter the radiation content seen in the CMB while having a negligible effect on BBN. Here we quantify this difference and explore the intermediate regime by examining particles decaying during BBN, i.e., particle lifetimes τₓ satisfying 0.1 sec < τₓ < 1000 sec. We calculate the change in the effective number of neutrino species, Neff, as measured by the CMB, ΔNCMB, and the change in the effective number of neutrino species as measured by BBN, ΔNBBN, as a function of the decaying particle initial energy density and lifetime, where ΔNBBN is defined in terms of the number of additional two-component neutrinos needed to produce the same change in the primordial helium-4 abundance as our decaying particle. As expected, for short lifetimes (τₓ < 0.1 sec), the particles decay before the onset of BBN, and ΔNCMB = ΔNBBN, while for long lifetimes (τₓ > 1000 sec), ΔNBBN is dominated by the energy density of the nonrelativistic particles before they decay, so that ΔNBBN remains nonzero and becomes independent of the particle lifetime. By varying both the particle energy density and lifetime, one can obtain any desired combination of ΔNBBN and ΔNCMB, subject to the constraint that ΔNCMB >= ΔNBBN. We present limits on the decaying particle parameters derived from observational constraints on ΔNCMB and ΔNBBN.