Gravothermalizing into primordial black holes, boson stars, and cannibal stars

TL;DR

This paper demonstrates that an early matter-dominated era (EMDE) driven by self-interacting hidden-sector particles can trigger gravothermal collapse in halos, producing primordial black holes (PBHs) as well as exotic objects like cannibal stars and boson stars, without requiring enhanced curvature perturbations. Using a simple real-scalar toy model with a quartic self-interaction, it derives halo formation criteria, gravothermal time scales, and the possible end states (PBHs, cannibal stars, boson stars) across EMDE parameter space. The authors compute PBH abundances, mass ranges, and observational constraints, showing asteroid-mass PBHs can naturally arise but are tightly constrained by CMB/BBN unless cannibal heating is suppressed; they further explore how maximal gravothermal accretion expands the PBH-forming window. Overall, the work reveals a rich phenomenology from gravothermal evolution in the early universe and provides a framework to probe EMDE scenarios through PBH and exotic-object signatures.

Abstract

Very little is known about the cosmological history from after the end of inflation until Big Bang Nucleosynthesis. Various well-motivated models predict that the universe could have undergone a period of matter domination in this early epoch. We demonstrate that if the particles causing matter domination have self-interactions, they can form halos that undergo a gravothermal collapse. We thus propose a novel scenario for the formation of primordial black holes, which in particular can lie within the asteroid-mass range. We also find that it is not only black holes that can form in the aftermath of a gravothermal evolution. We show that number-changing annihilations of the particles can create sufficient heat to halt the gravothermal evolution, thus forming a ``cannibal star''. Likewise, the pressure from the particle's repulsive self-interactions can form a boson star during a gravothermal evolution. Thus, our study highlights that structure formation in the early universe can have a rich phenomenology.

Figures (4)

• Figure 1: Scale factor during EMDE when perturbation modes with fixed comoving length scales ($k^{-1}$) enter the horizon (blue line), become non-linear and form halos (purple), and when the corresponding halos undergo gravothermal collapse (red). Here we use $\lambda = 10^{-1}$, $T_{\mathrm{rh}} = 100\, \mathrm{MeV}$, and $a_{\mathrm{rh}}/a_{\mathrm{i}} = 10^{15}$.
• Figure 2: Fraction of dark matter density in PBHs $f_{\rm BH}$, as a function of PBH mass $M_{\mathrm{BH}}$, for a fixed parameter set of $\lambda = 10^{-1}$, $T_{\mathrm{rh}} = 100\, \mathrm{MeV}$, and $a_{\mathrm{rh}}/a_{\mathrm{i}} = 10^{15}$. The red line shows $f_{\rm BH}$ assuming negligible black hole accretion, while the purple line assumes maximal accretion. Constraints on evaporating PBHs from CMB and BBN Carr:2009jmAcharya:2020jbv are shown by the blue and green regions, respectively. The vertical dashed lines mark the threshold masses needed for the core to overcome cannibal heating or pressure from the $\phi^4$ interaction and form a black hole. See the text for details.
• Figure 3: Consequences of gravothermal catastrophe in terms of reheat temperature $T_{\rm rh}$, and duration of EMDE $a_{\rm rh}/a_i$, with minimal gravothermal accretion. The self-coupling $\lambda$ is varied in the left and right panels, while cannibal annihilations are assumed to be negligible. Top Panels: The gray regions are excluded by requiring EMDE to be after inflation and before BBN. Gravothermal collapse does not occur on the left side of the line labeled "No Coll." All collapsing halos on the left of "Opt Thick" are initially optically thick. In the orange region, all halos collapse into boson stars; these are supported by the repulsive self-interaction above "B$\star$," and also by the quantum pressure above "Quantum Pressure." PBHs form in the region shown in various shades of blue. Bottom Panels: Zoom-in of the region where PBHs form. The white dashed contours show the PBH fraction in dark matter, $\log_{10} f_{\mathrm{BH}}$, while the gray dot-dashed and dashed contours respectively show the minimum ($M_-$) and maximum ($M_+$) PBH masses. The PBHs overdominate the present universe in the region labeled "$f_{\mathrm{BH}} > 1$," while the region with "CMB+BBN" is ruled out by CMB and BBN constraints on evaporating PBHs. The light blue region produces PBHs that are not in conflict with observations. See the text for details.
• Figure 4: Consequences of gravothermal catastrophe with maximal gravothermal accretion. The meanings of the labels and colours are the same as in fig. \ref{['fig:nocan_abundance']}, except for that the white dot-dashed contours here show the PBH abundance relative to the SM particles upon evaporation, $\log_{10} \kappa_{\mathrm{BH}}$. Top Panels: Parameter space assuming negligible cannibal annihilations. In the region shown in various shades of blue, PBHs are produced either from the direct gravothermal collapse of halos or from the collapse of boson stars. In the striped blue region, PBHs come to dominate the universe and evaporate before BBN. On the left of the "B$\star$ Surv" line, none of the boson stars collapse into PBHs. Bottom Panels: Parameter space in the presence of cannibal annihilations. In the blue-shaded regions, PBHs are also formed from the collapse of cannibal stars. On the left of the "C$\star$ Surv" line, none of the cannibal stars collapse into PBHs.