Dark Radiation from Particle Decays during Big Bang Nucleosynthesis

TL;DR

This work probes how a decaying massive relic can source dark radiation that affects the CMB and BBN differently. By modeling the decay as a transfer from a nonrelativistic X density to invisible relativistic radiation and computing the resulting $N_{eff}$ shifts, the authors establish both analytic and numerical relations between $ΔN_{CMB}$ and $ΔN_{BBN}$ as functions of the initial abundance $Y_X m_X$ and lifetime $τ_X$, including a regime where $ΔN_{CMB}$ rises as the square root of $τ_X$. They map these results to BBN helium constraints using the Kawano–Wagoner BBN code with $η = 6.1×10^{-10}$ to obtain $ΔN_{BBN}$, showing that short lifetimes yield $ΔN_{CMB} = ΔN_{BBN}$ while long lifetimes produce a $ΔN_{BBN}$ that is effectively $τ_X$-independent but nonzero due to the pre-decay nonrelativistic energy density. Observational bounds on $ΔN_{CMB}$ and $ΔN_{BBN}$ delineate an allowed region in $(τ_X, Y_X m_X)$, with the key constraint $ΔN_{CMB} \,≥\, ΔN_{BBN}$ providing falsifiability for this class of models. The results offer a coherent framework to interpret potential hints of dark radiation and guide future constraints on decaying relic scenarios.

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}.

Figures (3)

• Figure 1: Contour plot of $\Delta N_{CMB}$, the change in the effective number of neutrinos determined by CMB observations due to a decaying particle with lifetime $\tau_X$ and energy density prior to decay parametrized in terms of $Y_X m_X$, where $Y_X$ is the initial number density of the particle relative to entropy density, and $m_X$ is the particle mass. Curves correspond to, from bottom to top, $\Delta N_{CMB} = 0.1, 0.2, 0.3, 0.4, 0.7, 1.0, 1.5, 2.0$.
• Figure 2: Contour plot of $\Delta N_{BBN}$, the change in the effective number of neutrinos giving the same change in the primordial $^4$He abundance as a decaying particle with lifetime $\tau_X$ and energy density prior to decay parametrized in terms of $Y_X m_X$, where $Y_X$ is the initial number density of the particle relative to entropy density, and $m_X$ is the particle mass. Curves correspond to, from bottom to top, $\Delta N_{BBN} = 0.1, 0.2, 0.3, 0.4, 0.7, 1.0, 1.5, 2.0$.
• Figure 3: Observational constraints from the CMB and BBN in the $\tau_X$, $Y_X m_X$ plane, where $\tau_X$ is the decaying particle lifetime, $Y_X$ is the initial number density of the particle relative to entropy density, and $m_X$ is the particle mass. The region between the two solid curves is allowed by the CMB bounds on $N_{eff}$ from Ref. Arch, while the area below the dashed curve is the allowed region from BBN limits on $N_{eff}$ given by Ref. mangano2. The shaded (yellow) region satisfies both constraints.