Dark radiation from particle decays during big bang nucleosynthesis

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 ₗ satisfying 0. 1 sec<ₗ<1000 sec. We calculate the change in the effective number of neutrino species, N₄₅₅, as measured by the CMB, N₂₌₁, and the change in the effective number of neutrino species as measured by BBN, N₁₁₍, as a function of the decaying particle initial energy density and lifetime, where N₁₁₍ is defined in terms of the number of additional two-component neutrinos needed to produce the same change in the primordial ^4He abundance as our decaying particle. As expected, for short lifetimes (ₗ0. 1 sec), the particles decay before the onset of BBN, and N₂₌₁=N₁₁₍, while for long lifetimes (ₗ1000 sec), N₁₁₍ is dominated by the energy density of the nonrelativistic particles before they decay, so that N₁₁₍ 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 N₁₁₍ and N₂₌₁, subject to the constraint that N₂₌₁N₁₁₍. We present limits on the decaying particle parameters derived from observational constraints on N₂₌₁ and N₁₁₍.