How Primordial Black Holes Change BBN

TL;DR

This work explores how Hawking radiation from primordial black holes (PBHs) can modify Big Bang Nucleosynthesis (BBN) by injecting entropy and altering reaction rates. Using a bottom-up approach, the authors embed PBH evaporation into a nuclear-reaction network (burst) and compute PBH mass fractions $\beta(M)$ as functions of the scalar spectral index $n_s$ and its running ${dn_s}/{d\ln k}$ for PBH masses in the range $10^{8}$–$10^{13}\, ext{g}$. A key result is a threshold near $M \approx 10^{10}\, ext{g}$ that splits two distinct BBN behaviors: for $M \gtrsim 10^{10}\, ext{g}$, the helium-4 mass fraction $Y_{\mathrm{P}}$ grows monotonically with $\beta$ due to faster expansion, while for $M \lesssim 10^{10}\, ext{g}$, $Y_{\mathrm{P}}$ shows non-monotonic, oscillatory dependence tied to evaporation timing and reaction rates. The study also shows that to match the observed comoving entropy per baryon, the early-universe entropy must be lower in PBH scenarios, highlighting the importance of consistent entropy evolution in PBH–BBN cosmologies and providing a framework for constraining PBHs with primordial abundances.

Abstract

Primordial Black Holes (PBHs) provide a powerful probe of early-universe physics, linking inflationary fluctuations to observable cosmological phenomena. In this work, we use a bottom-up approach to study how PBHs with masses in the range $10^{8} \leq M \leq 10^{13}\,\mathrm{g}$ modify Big Bang Nucleosynthesis (BBN) through Hawking radiation. We incorporate PBH evaporation into a reaction-network code to evaluate its impact on light-element abundances. Our analysis shows that PBH evaporation acts as an entropy injection mechanism, increasing the comoving entropy density. To reproduce the observed comoving entropy density per baryon $(s/n_{\mathrm{b}})$ from the CMB, BBN simulations must therefore begin with a smaller initial entropy than in the standard scenario without PBHs. The results also reveal a threshold near $M \approx 10^{10}\,\mathrm{g}$ that separates two distinct regimes of BBN behavior. As an example, for $M \geq 10^{10}\,\mathrm{g}$, the $^4{\mathrm{He}}$ mass fraction $Y_{\mathrm{P}}$ increases monotonically with $β$, driven by the enhanced Hubble expansion from PBH energy density. In contrast, for $M \leq 10^{10}\,\mathrm{g}$, $Y_{\mathrm{P}}$ exhibits non-monotonic behavior shaped by the timing of PBH evaporation and its influence on nuclear reaction rates. These findings highlight the sensitivity of BBN to PBH evaporation and establish a framework for understanding how PBH populations influence the thermal history of the early universe.

Figures (11)

• Figure 1: Left: PBH mass fraction $\beta$ without a running $n_s$, from \ref{['eq:3.4']}, at $T=30\,\mathrm{MeV}$, shown for different values of the scalar spectral index $n_s$. When $n_s < 1.38$, PBH formation is negligible ($\log_{10}\beta \lesssim -10$) within the relevant mass range. Right: Contour plot of the PBH mass fraction $\log_{10}\beta(M = 10^{10}\,\mathrm{g})$ as a function of $n_s$ and its running $dn_s/d\ln(k)$ at $T = 30\,\mathrm{MeV}$.
• Figure 2: Contour plots showing regions of interest where $0 \geq \log_{10}(\beta) \geq -10$ for different PBH masses, evaluated at a cosmic temperature of $T = 30\,\mathrm{MeV}$. As the PBH mass increases, the region of interest broadens and shifts toward higher values of the scalar spectral index $n_s$. Heavier PBHs form more efficiently in spectra with larger $n_s$, consistent with the behavior observed in Fig. \ref{['fig01']}.
• Figure 3: Evolution of the comoving entropy density per baryon, $(s/n_{\mathrm{b}})$ as a function of comoving temperature quantity, $T_{\mathrm{cm}}$, in the case $n_s = 1.3$ and $\mathrm{d} n_s/\mathrm{d} \ln(k) = 5\times10^{-3}$. Each curve represents a different mass and would have a different initial value of $\beta$.
• Figure 4: Mass fraction of $^4{\mathrm{He}}$ ($Y_{\mathrm{P}}\xspace$, red, left axis) and the PBH mass fraction ($\log_{10} \beta$ at $T = 30\,\mathrm{MeV}$, blue, right axis) as functions of PBH mass $M$ for multiple values of $n_s$ and $\mathrm{d}n_s/ \mathrm{d} \ln(k) = 5\times10^{-3}$.
• Figure 5: Same as Fig. \ref{['fig04']} but for the deuterium mass fraction $X_{\mathrm{D}\xspace}$.