Dark radiation from particle decays during big bang nucleosynthesis

Abstract

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 ${\ensuremath{\tau}}_{X}$ satisfying $0.1\text{ }\text{ }\mathrm{sec}<{\ensuremath{\tau}}_{X}<1000\text{ }\text{ }\mathrm{sec}$. We calculate the change in the effective number of neutrino species, ${N}_{\mathrm{eff}}$, as measured by the CMB, $\ensuremath{\Delta}{N}_{\mathrm{CMB}}$, and the change in the effective number of neutrino species as measured by BBN, $\ensuremath{\Delta}{N}_{\mathrm{BBN}}$, as a function of the decaying particle initial energy density and lifetime, where $\ensuremath{\Delta}{N}_{\mathrm{BBN}}$ is defined in terms of the number of additional two-component neutrinos needed to produce the same change in the primordial $^{4}\mathrm{He}$ abundance as our decaying particle. As expected, for short lifetimes (${\ensuremath{\tau}}_{X}\ensuremath{\lesssim}0.1\text{ }\text{ }\mathrm{sec}$), the particles decay before the onset of BBN, and $\ensuremath{\Delta}{N}_{\mathrm{CMB}}=\ensuremath{\Delta}{N}_{\mathrm{BBN}}$, while for long lifetimes (${\ensuremath{\tau}}_{X}\ensuremath{\gtrsim}1000\text{ }\text{ }\mathrm{sec}$), $\ensuremath{\Delta}{N}_{\mathrm{BBN}}$ is dominated by the energy density of the nonrelativistic particles before they decay, so that $\ensuremath{\Delta}{N}_{\mathrm{BBN}}$ 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 $\ensuremath{\Delta}{N}_{\mathrm{BBN}}$ and $\ensuremath{\Delta}{N}_{\mathrm{CMB}}$, subject to the constraint that $\ensuremath{\Delta}{N}_{\mathrm{CMB}}\ensuremath{\ge}\ensuremath{\Delta}{N}_{\mathrm{BBN}}$. We present limits on the decaying particle parameters derived from observational constraints on $\ensuremath{\Delta}{N}_{\mathrm{CMB}}$ and $\ensuremath{\Delta}{N}_{\mathrm{BBN}}$.