Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the seeds of Galaxies

TL;DR

This work proposes that dark matter consists of a broad spectrum of massive primordial black holes formed from large curvature perturbations generated during a mild waterfall phase at the end of hybrid inflation. The authors develop a two-field potential that yields a red-tilted CMB spectrum while producing a broad peak in the curvature power spectrum on smaller scales, enabling PBH formation without violating Planck constraints. They compute PBH mass functions and abundances, showing that with a narrow window for the peak amplitude controlled by Π^2, PBH can constitute dark matter and potentially seed supermassive black holes, especially after growth by merging. The model makes distinctive predictions, including observable CMB distortions from enhanced small-scale power and a population of stellar-mass PBHs in nearby galaxies, which can be tested by future 21 cm, X-ray, and gravitational-wave experiments.

Abstract

In this paper we present a new scenario where massive Primordial Black Holes (PBH) are produced from the collapse of large curvature perturbations generated during a mild waterfall phase of hybrid inflation. We determine the values of the inflaton potential parameters leading to a PBH mass spectrum peaking on planetary-like masses at matter-radiation equality and producing abundances comparable to those of Dark Matter today, while the matter power spectrum on scales probed by CMB anisotropies agrees with Planck data. These PBH could have acquired large stellar masses today, via merging, and the model passes both the constraints from CMB distortions and micro-lensing. This scenario is supported by Chandra observations of numerous BH candidates in the central region of Andromeda. Moreover, the tail of the PBH mass distribution could be responsible for the seeds of supermassive black holes at the center of galaxies, as well as for ultra-luminous X-rays sources. We find that our effective hybrid potential can originate e.g. from D-term inflation with a Fayet-Iliopoulos term of the order of the Planck scale but sub-planckian values of the inflaton field. Finally, we discuss the implications of quantum diffusion at the instability point of the potential, able to generate a swiss-cheese like structure of the Universe, eventually leading to apparent accelerated cosmic expansion.

Figures (5)

• Figure 1: Limits on the abundance of PBH today, from extragalactic photon background (orange), femto-lensing (red), micro-lensing by MACHO (green) and EROS (blue) and CMB distortions by FIRAS (cyan) and WMAP3 (purple). The constraints from star formation and capture by neutron stars in globular clusters are displayed for $\rho_{\mathrm{DM}}^{\mathrm{Glob. Cl.}} = 2 \times 10^3 \ \mathrm{GeV cm^{-3}}$ (brown). The black dashed line corresponds to a particular realization of our scenario of PBH formation. Figure adapted from Capela:2013yf.
• Figure 2: Power spectrum of curvature perturbations for parameters $M = \phi_{\mathrm c} = 0.1 M_{\rm P}$, $\mu_1 = 3 \times 10^5 M_{\rm P}$. The solid curve is obtained by integrating numerically the exact multi-field background and linear perturbation dynamics. The dashed blue line is obtained by using the $\delta N$ formalism. The dotted blue line uses the $\delta N$ formalism with the approximation of Eq. (\ref{['eq:Pzeta_exit_in_phase1']}).
• Figure 3: Power spectrum of curvature perturbations for parameters values $M = 0.1 M_{\rm P}$, $\mu_1 = 3 \times 10^5 M_{\rm P}$ and $\phi_{\mathrm c} = 0.125 M_{\rm P}$ (red), $\phi_{\mathrm c} = 0.1 M_{\rm P}$ (blue) and $\phi_{\mathrm c} = 0.075 M_{\rm P}$ (green), $\phi_{\mathrm c} = 0.1 M_{\rm P}$ (blue) and $\phi_{\mathrm c} = 0.05 M_{\rm P}$ (cyan). Those parameters correspond respectively to $\Pi^2 = 375 / 300 / 225/150$. The power spectrum is degenerate for lower values of $M,\phi$ and larger values of $\mu_1$, keeping the combination $\Pi^2$ constant. For larger values of $M, \phi_{\mathrm c}$ the degeneracy is broken: power spectra in orange and brown are obtained respectively for $M = \phi_{\mathrm c} = M_{\rm P}$ and $\mu_1 = 300 M_{\rm P} / 225 M_{\rm P}$. Dashed lines assume $\psi_{\mathrm c} = \psi_0$ whereas solid lines are obtained after averaging over 200 power spectra obtained from initial conditions on $\psi_{\mathrm c}$ distributed according to a Gaussian of width $\psi_0$. The power spectra corresponding to these realizations are plotted in dashed light gray for illustration. The $\Lambda$ parameter has been fixed so that the spectrum amplitude on CMB anisotropy scales is in agreement with Planck data. The parameter $\mu_2 = 10 M_{\rm P}$ so that the scalar spectral index on those scales is given by $n_{\mathrm s} = 0.96$.
• Figure 4: PBH abundances at the time of formation $\beta^{\mathrm{form}}(M)$ (top panel) and at matter-radiation equality $\beta(M, N_{eq})$ (bottom panel). The color scheme corresponds to the parameters given in Fig. \ref{['fig:Pzeta']}. The blue dashed curve is obtained for $\Pi^2 = 300$ but with $M = \phi_{\mathrm c} = 0.01 M_{\rm P}$ and $\mu_1 = 3 \times 10^8 M_{\rm P}$, illustrating that PBH masses can be made arbitrarily large for a given value of $\Pi^2$. The critical curvature $\zeta_c$ has been set so that the right amount of dark matter has been produced at matter-radiation equality. Values of $\zeta_c$ are reported in Table \ref{['tab:omegaPBH']}
• Figure 5: Total spectrum of CMB distortions for same parameters and colors as in Figs. \ref{['fig:Pzeta']} and \ref{['fig:betaspectrumzeq']} (brown and green curves are superimposed, undistinguishable from standard inflation with $n_{\mathrm s} = 0.961$ and no running). The $1\sigma$ limits for PIXIE and PRISM, see Eqs. (\ref{['sensitivity:PIXIE']}) and (\ref{['sensitivity:PRISM']}), are also represented.