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, Neff, 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 DNBBN 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 (τ_X < 0.1 sec), the particles decay before the onset of BBN, and DNCMB = DNBBN,

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 N_BBN and ΔN_CMB, subject to the constraint that

DNCMB N_BBN. We present limits on the decaying particle parameters derived from

observational constraints on ΔN_CMB, and N_BBN.