Primordial Black Holes Evaporating before Big Bang Nucleosynthesis

TL;DR

This work addresses how primordial black holes (PBHs) evaporating before Big Bang nucleosynthesis (BBN) can modify the primordial light-element abundances. It develops a transparent framework that couples PBH Hawking radiation, hadronization, meson-driven neutron-to-proton conversions, and nucleon annihilation to the standard BBN dynamics, and provides public code for reproducible analysis. The main result is a mass-threshold around $m_{\rm BH,i} \gtrsim 10^{9}$ g for observable effects, with a turning point near $2\times 10^{9}$ g, and BBN constraints on the initial mass fraction $\beta$ in the range $10^{-17}$ to $10^{-19}$ for PBHs with $m_{\rm BH,i} \in [10^{9},10^{10}]$ g. The findings refine the landscape of PBH-BBN constraints by improving the treatment of hadron emissivity and PBH-induced hadronic processes, and the provided code enables straightforward updates as nuclear and cosmological inputs evolve. This work strengthens BBN as a probe of sub-Planckian PBHs and equips the community with a reproducible tool for future refinements, including potential post-BBN PBH scenarios in companion analyses.

Abstract

Primordial black holes (PBHs) formed from the collapse of density fluctuations provide a unique window into the physics of the early Universe. Their evaporation through Hawking radiation around the epoch of Big Bang nucleosynthesis (BBN) can leave measurable imprints on the primordial light-element abundances. In this work, we analyze in detail the effects of PBHs evaporating before BBN, with various intermediate steps understood analytically, and obtain the BBN constraint on PBHs within a transparent and reproducible framework. We find that, to produce observable effects on BBN, the PBH mass must exceed $10^{9}$ g, a threshold higher than that reported in some earlier studies. Slightly above $10^{9}$ g, the BBN sensitivity rapidly increases with the mass and then decreases, with the turning point occurring at $2\times10^{9}$ g. For PBHs in the mass range $[10^{9},\ 10^{10}]$ g, current measurements of BBN observables set an upper bound on the initial mass fraction parameter $β$ ranging from $10^{-17}$ to $10^{-19}$. To facilitate future improvements, we make our code publicly available, enabling straightforward incorporation of updated nuclear reaction rates, particle-physics inputs, and cosmological data.

Figures (7)

• Figure 1: The energy density of PBHs $\rho_{\text{BH}}$ compared with the neutrino energy density $\rho_{\nu}$. Here solid lines are obtained by numerically solving the evolution of $\rho_{\text{BH}}$; dashed lines represent the analytical estimate in Eq. \ref{['eq:-28']}. The vertical dotted line indicates the temperature of nucleosynthesis.
• Figure 2: Hadronic production rates of PBHs obtained from BlackHawk (solid lines) and analytical estimates (dashed lines). The solid lines are not extended to $m_{{\rm BH}}<10^{9}$ g because below this mass, we are unable to obtain BlackHawk results unaffected by the energy limit imposed on partons---see the main text for details.
• Figure 3: The number densities of hadrons obtained by numerically solving the corresponding Boltzmann equations (solid lines) compared with the analytical estimates using Eq. \ref{['eq:-37']} (dashed lines). The shown example assumes $m_{{\rm BH},i}=6\times10^{9}$ g and $\beta=10^{-16}$.
• Figure 4: Evolution of $X_{n}$ in the presence of PBH evaporation. The left panel presents values of $X_{n}$ and the right panel shows the ratio $X_{n}/X_{n}^{{\rm (SBBN)}}$ where $X_{n}^{({\rm SBBN)}}$ denotes $X_{n}$ in standard BBN.
• Figure 5: The 2 $\sigma$ C.L. constraint on PBHs from the BBN observable $Y_{P}$ obtained in this work (solid line) compared with constraints obtained in earlier studies (dashed lines), including Carr et al. 2020 Carr:2020gox, Kohri et al. 2000 Kohri:1999ex, Keith et al. 2020 Keith:2020jww.