Dark Radiation from Particle Decays during Big Bang Nucleosynthesis

Abstract

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 τ_X satisfying 0.1 sec < τ_X < 1000 sec. We calculate the change in the effective number of neutrino species, N_{eff}, as measured by the CMB, ΔN_{CMB}, and the change in the effective number of neutrino species as measured by BBN, ΔN_{BBN}, as a function of the decaying particle initial energy density and lifetime, where ΔN_{BBN} 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 (τ_X < 0.1 sec), the particles decay before the onset of BBN, and ΔN_{CMB} = ΔN_{BBN}, while for long lifetimes (τ_X > 1000 sec), ΔN_{BBN} is dominated by the energy density of the nonrelativistic particles before they decay, so that ΔN_{BBN} 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 ΔN_{BBN} and ΔN_{CMB}, subject to the constraint that ΔN_{CMB} >= ΔN_{BBN}. We present limits on the decaying particle parameters derived from observational constraints on ΔN_{CMB} and ΔN_{BBN}.