When Primordial Black Holes Absorb During the Early Universe

TL;DR

This paper demonstrates that PBHs in the early Universe can undergo substantial mass growth through thermal absorption from the surrounding plasma, altering their evolution beyond standard Hawking evaporation. By implementing frequency-dependent absorption cross sections and a master equation that couples absorption to evaporation, the authors identify a critical collapse efficiency γ_c ≈ 0.395 that marks a transition to runaway growth when exceeded. The resulting mass growth extends PBH lifetimes, lowering the reheating temperature and shifting DM production and relic-bounds, with corrections ranging from modest to several orders of magnitude depending on the formation mass and γ. Overall, thermal absorption emerges as a crucial ingredient for accurate PBH cosmology, reshaping viable parameter spaces for PBHs as DM and as reheating agents, with clear avenues for further work on rotating PBHs and GW signatures.

Abstract

We study the evolution of primordial black holes (PBHs) formed in the early universe in the presence of a surrounding thermal bath. By incorporating the effects of thermal absorption, we show that PBHs can undergo significant mass growth, leading to extended lifetimes and substantial deviations from the standard Hawking evaporation scenario. We find a critical collapse efficiency, $γ_{\rm c} \simeq 0.395$, above which the PBH mass grows without bound. This correction has profound implications for both PBH-induced reheating and dark matter (DM) production. Specifically, we find that the reheating temperature can be suppressed, and the DM parameter space for the PBH reheating scenario can undergo $\mathcal{O}(10)$-$\mathcal{O}(10^4)$ corrections, depending on the PBH formation mass and collapse efficiency. Moreover, our results significantly shift the parameter space in which PBHs can account for the entirety of the DM. To the best of our knowledge, this is the first comprehensive phenomenological study to incorporate thermal absorption into PBH evolution and quantify its impact on cosmological observables.

Figures (5)

• Figure 1: Evolution of the PBH mass, normalized to its formation mass $M_{\rm in}$, for $M_{\rm in}=1$g, as function of the scale factor relative to the formation time, $\frac{a}{a_{\rm in}}$, for four different values of the parameter $\gamma$, which denotes the ratio of the horizon mass to the PBH mass at formation, see Eq. (\ref{['Eq:min']}). The red dotted line represents the standard case with $\gamma = 0.2$, while the black dot-dashed line shows the diverging solution for $\gamma=0.396$, values slightly above the critical threshold, $\gamma_{\rm c}=32/81\sim 0.395$, see Eq.(\ref{['Eq:deltac']}).
• Figure 2: Evolution of the PBH mass, normalized to its formation mass, as a function of time for different values of $\gamma$ is shown. The blue solid, gree dashed, and red dotted lines correspond to cases where radiation absorption is included, while the red dot-dashed line represent scenarios where absorption is neglected or $\gamma$ is chosen such a way that absorption has no effect. In all plots, the PBH formation mass are selected so that evaporation occurs around the BBN timescale, i.e., 1 second.
• Figure 3: Evolution of the PBH mass, normalized to its formation mass $M_{\rm in}$, for different values of $M_{\rm in}$ (1g, $10^2$g, $10^4$g and $10^6$g), as function of the scale factor relative to the formation time, $\frac{a}{a_{\rm in}}$.
• Figure 4: Viable parameter space in the $(M_{\rm in}, m_j)$ plane for $\beta > \beta_c$. The black contours indicate regions consistent with the observed DM relic abundance. The dashed and solid lines correspond to $\gamma = 0.3$ and $\gamma = 0.39$, respectively in the presence of PBH mass growth due to radiation absorption. For comparison, the standard scenario without absorption is also shown by the dot-dashed black line. Shaded regions are excluded due to DM overproduction, while the white regions are viable but require an additional production mechanism to match the observed relic abundance. BBN and CMB constraints exclude the red and magenta-shaded areas, respectively. The CMB bounds are derived from the horizon size at the end of inflation, assuming a de Sitter-like expansion, and incorporate the upper limit on the Hubble parameter set by the tensor-to-scalar ratio $r < 0.036$, as constrained by Planck 2018 and BICEP2/Keck Array observations BICEP:2021xfzBICEP2:2015nss.
• Figure 5: Constraints on the PBH dark matter fraction $f_{\rm PBH}$ as a function of the initial mass $M_{\rm in}$. The dot-dashed curve represents the scenario with Hawking evaporation only, while the solid and dashed curves include the effect of mass growth due to thermal absorption for $\gamma = 0.30$ and $\gamma = 0.39$, respectively. The shaded regions indicate excluded parameter space from various observations: evaporation (red), microlensing (blue), and gravitational waves (magenta). The black lines denote the minimum PBH mass above which they remain stable today.