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