Constraining the Coexistence of Freeze-in Dark Matter and Primordial Black Holes

TL;DR

The paper addresses the question of how primordial black holes can coexist with freeze-in dark matter (FIMPs) by deriving indirect-detection bounds on the PBH fraction $f_{ m PBH}$ across IR, UV, Boltzmann-suppressed freeze-in, including superheavy DM. It develops a detailed halo-formation framework around PBHs where FI-produced FIMPs form halos with density profiles shaped by the FI history, kinetic properties, and annihilations, and then translates these halo properties into gamma-ray constraints using Fermi-LAT data. The results show that in many models, PBHs with $f_{ m PBH}$ as small as a percent can be constrained, with some regimes yielding bounds stronger than PBH-only limits and even covering asteroid-mass windows; the strength and character of the bounds depend on the FI type, mediator structure (e.g., $Z'$), and DM mass. Overall, the work demonstrates that indirect-detection probes can effectively test mixed PBH–FIMP scenarios and outlines several promising extensions, including keV-scale FIMPs, other astrophysical observables, and non-minimal hidden-sector dynamics.

Abstract

Particle dark matter and primordial black holes (PBH) might coexist with appreciable cosmic abundances, with both contributing to the observed dark matter density $Ω_{\rm DM}$. Large populations of PBH (with $Ω_{\rm PBH}\sim Ω_{\rm DM}$) are tightly constrained for PBH heavier than $10^{-11} M_\odot$. However, large fractional abundances with $ f_{\rm PBH}\simeq Ω_{\rm PBH}/Ω_{\rm DM}\sim0.01$ are consistent with the limits on PBH for a wide range of PBH masses. Scenarios with significant populations of both particle dark matter and PBH are intriguing. Notably, if the particle dark matter has interactions with the Standard Model, new constraints arise due to pair-annihilations that are enhanced by the PBHs, resulting in dark matter indirect detection constraints on $f_{\rm PBH}$. Here we derive the bounds on mixed scenarios in which PBHs coexist with particle dark matter whose relic abundance is set via freeze-in (``FIMPs''). We show that while the restrictions on $f_{\rm PBH}$ are less constraining for FIMPs than WIMPs, modest bounds still arise for large classes of models. We examine both IR and UV freeze-in scenarios, including the case of ``superheavy'' particle dark matter with PeV scale mass.

Figures (7)

• Figure 1: Halo profiles for 1 TeV dark matter around a PBH of mass $M_{\bullet} = 10^{-6} M_{\odot}$. The left panel represents the halo profile for dark matter for the dimension 4 freeze-in model for two values of the mediator mass $M_{Z'} = 500$ GeV and $M_{Z'} = 750$ GeV, and a DM-$Z'$ coupling value of $g = 10^{-4}$. The right panel represents the same for a dimension-5 UV freeze-in model via a non-renormalizable operator. We use two values of $\Lambda$ (the energy scale of new physics for UV freeze in) with the corresponding $T_{\rm RH}$ values shown as well. In both panels, halo profiles for freeze-out dark matter (see e.g. Chanda:2022hls) are shown as dashed lines for comparison. Observe that the central plateau region is much smaller than freeze-out dark matter for freeze-in dark matter in both panels.
• Figure 2: Dimension 4. We assume FIMP freeze-in via a $Z'$ with $M_{Z'} < 2 m_{\rm DM}$, involving a renormalisable interaction. The plots show the maximum PBH fractional abundance consistent with Fermi-LAT extragalactic $\gamma$-ray background, as a function of PBH mass $M_{\bullet}$. Since $M_{Z'} < 2 m_{\rm DM}$, in both panels the primary freeze-in channel is via $f \bar{f} \rightarrow X \bar{X}$. Both panels correspond to Case A.i discussed in the text. The combination $g\lambda$ sets the relic abundance, cf. eq. (\ref{['eq:3.7']}). The grey regions are the standard constraints on PBH coming from evaporations, gravitational waves, lensing, and CMB distortions (see e.g. Carr:2020gox). Left Panel. For a FIMP-$Z'$ coupling value of $g = 10^{-4}$ (solid lines), we have t-channel annihilation $X \bar{X} \rightarrow Z'Z' \rightarrow b \bar{b} b \bar{b}$ as the dominant annihilation channel for both values of $M_{Z'}$, while for the lines corresponding to $g = 10^{-9}$ (dashed), the s-channel annihilation $X \bar{X} \rightarrow b \bar{b}$ is dominant. Right Panel. For $m_{\rm DM} = 1 {\rm ~ TeV}$, we only get constraints on $f_{{\rm PBH}}$ when the t-channel annihilation is dominant, i.e. when $M_{Z'} < m_{\rm DM}$ and $g \lesssim 10^{-5}$. In both panels, we check that the couplings are not so large that the FIMPs come into equilibrium with the visible sector. Specifically, for the values of the $Z'$ mass we find that avoiding equilibration restricts $g \lesssim 10^{-3}$ (with $\lambda\sim10^{-11}/g$).
• Figure 3: Dimension 4. As Figure \ref{['fig:dim4']} but with $M_{Z'} > 2 m_{\rm DM}$. Left [Case A.ii]. Freeze-in occurs via $f \bar{f} \rightarrow X \bar{X}$, the FIMP relic density is determined by eq. (\ref{['eq:3.10']}) which fixes $g$. Right [Case B]. Freeze-in of $X$ occurs via the two-step process $f \bar{f} \rightarrow Z'$ and $Z'\rightarrow X \bar{X}$, the FIMP relic density is set by eq. (\ref{['eq:3.12']}) which fixes $\lambda$. In both cases, one coupling is fixed by the relic abundance, and we are free to choose the other. We confirm that the parameters taken do not lead to sector equilibration.
• Figure 4: Dimension 5.$f_{{\rm max}}$ vs $M_{\bullet}$ constraints for freeze-in freeze-in involving a dimension 5 operator $\frac{1}{\Lambda} \phi^{\dagger} \phi \bar{f} f$, where $\Lambda$ is the energy scale of new physics. We consider the generic s-wave cross-section for $\phi \phi^{\dagger} \rightarrow b \bar{b}$ annihilations. We take three values of $\Lambda$ and the corresponding $T_{{\rm RH}}$ values are shown in parentheses. This is calculated in the Boltzmann suppressed UV freeze-in regime, where we assume $T_{\rm max} \sim 50 T_{{\rm RH}}$, for standard UV freeze-in with $m_{\rm DM}<T_{\rm RH}$, there is no constraint. The left panel is for 100 GeV dark matter, and the right panel is for 1 TeV dark matter. In both panels, FIMP equilibration with the Standard Model bath is avoided provided $\Lambda \gtrsim 10^{9}$ GeV. PBH form prior to reheating in the parameter space left of the brown dashed line.
• Figure 5: Dimension 6.$f_{{\rm max}}$ vs $M_{\bullet}$ constraints for freeze-in involving a dimension 6 operator $\frac{1}{\Lambda^2} \bar{X} X \bar{f} f$. We consider the generic s-wave cross-section for $X \bar{X} \rightarrow b \bar{b}$ annihilations. Corresponding $T_{{\rm RH}}$ values to each value of $\Lambda$ are shown in parentheses. The left panel corresponds to 100 GeV dark matter, and the right panel corresponds to 1 TeV dark matter. We take three values of $\Lambda$ in both panels. As with dimension five for standard UV freeze-in with $m_{\rm DM}<T_{\rm RH}$ there are no constraints but for Boltzmann Suppressed UV freeze-in constraints can arise, here we take $T_{\rm max} \simeq 50 T_{{\rm RH}}$ as before. In both panels, one can avoid FIMP equilibration with the Standard Model bath provided $\Lambda \gtrsim 10^{6}$ GeV. PBH form prior to reheating in the parameter space left of the brown dashed line.