Massive primordial black holes from hybrid inflation as dark matter and the seeds of galaxies

Sébastien Clesse and Juan García-Bellido

Phys. Rev. D 92, 023524 – Published 16 July 2015

Abstract

In this paper we present a new scenario where massive primordial black holes (PBHs) 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 planetarylike masses at matter-radiation equality and producing abundances comparable to those of dark matter today, while the matter power spectrum on scales probed by cosmic microwave background (CMB) anisotropies agrees with Planck data. These PBHs could have acquired large stellar masses today, via merging, and the model passes both the constraints from CMB distortions and microlensing. 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 ultraluminous x-ray 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.

Received 9 March 2015

DOI:https://doi.org/10.1103/PhysRevD.92.023524

Authors & Affiliations

Sébastien Clesse^1,* and Juan García-Bellido^2,†

¹Namur Center of Complex Systems (naXys), Department of Mathematics, University of Namur, Rempart de la Vierge 8, 5000 Namur, Belgium
²Instituto de Física Teórica UAM-CSIC, Universidad Autonóma de Madrid, Cantoblanco, 28049 Madrid, Spain

^*sebastien.clesse@unamur.be
^†juan.garciabellido@uam.es

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Vol. 92, Iss. 2 — 15 July 2015

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Images

Figure 1
Limits on the abundance of PBHs today, from extragalactic photon background (orange line), femtolensing (red line), microlensing by MACHO (green line) and EROS (blue line) and CMB distortions by FIRAS (cyan line) and WMAP3 (purple line). The constraints from star formation and capture by neutron stars in globular clusters are shown for $ρ_{DM}^{Glob Cl} = 2 \times 1 0^{3} GeV {cm}^{- 3}$ (brown line). The black dashed line corresponds to a particular realization of our scenario of PBH formation. Figure adapted from [59].
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Figure 2
Power spectrum of curvature perturbations for parameters $M = ϕ_{c} = 0.1 M_{P}$ , $μ_{1} = 3 \times 1 0^{5} M_{P}$ . The solid curve is obtained by integrating numerically the exact multifield background and linear perturbation dynamics. The dashed blue line is obtained by using the $δ N$ formalism. The dotted blue line uses the $δ N$ formalism with the approximation of Eq. (31).
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Figure 3
Power spectrum of curvature perturbations for parameters values $M = 0.1 M_{P}$ , $μ_{1} = 3 \times 1 0^{5} M_{P}$ and $ϕ_{c} = 0.125 M_{P}$ (red - 1st curve from top), $ϕ_{c} = 0.1 M_{P}$ (blue - 3rd) and $ϕ_{c} = 0.075 M_{P}$ (green - 5th), and $ϕ_{c} = 0.05 M_{P}$ (cyan - 6th). Those parameters correspond respectively to $Π^{2} = 375 / 300 / 225 / 150$ . The power spectrum is degenerate for lower values of $M, ϕ$ and larger values of $μ_{1}$ , keeping the combination $Π^{2}$ constant. For larger values of $M, ϕ_{c}$ the degeneracy is broken: power spectra in orange (2nd curve from top) and brown (4th) are obtained respectively for $M = ϕ_{c} = M_{P}$ and $μ_{1} = 300 M_{P} / 225 M_{P}$ . Dashed lines assume $ψ_{c} = ψ_{0}$ whereas solid lines are obtained after averaging over 200 power spectra obtained from initial conditions on $ψ_{c}$ distributed according to a Gaussian of width $ψ_{0}$ . The power spectra corresponding to these realizations are plotted in dashed light gray for illustration. The $Λ$ parameter has been fixed so that the spectrum amplitude on CMB anisotropy scales is in agreement with Planck data. The parameter $μ_{2} = 10 M_{P}$ so that the scalar spectral index on those scales is given by $n_{s} = 0.96$ .
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Figure 4
PBH abundances at the time of formation $β^{form} (M)$ (top panel) and at matter-radiation equality $β (M, N_{eq})$ (bottom panel). The color scheme (gray scale) corresponds to the parameters given in Fig. 3. The blue dashed curve is obtained for $Π^{2} = 300$ but with $M = ϕ_{c} = 0.01 M_{P}$ and $μ_{1} = 3 \times 1 0^{8} M_{P}$ , illustrating that PBH masses can be made arbitrarily large for a given value of $Π^{2}$ . The critical curvature $ζ_{c}$ has been set so that the right amount of dark matter has been produced at matter-radiation equality. Values of $ζ_{c}$ are reported in Table 1.
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Figure 5
Total spectrum of CMB distortions for the same parameters and colors (gray scale) as in Figs. 3 and 4 (brown and green curves are superimposed, undistinguishable from standard inflation with $n_{s} = 0.961$ and no running). The $1 σ$ limits for PIXIE and PRISM [see Eqs. (60) and (61)] are also represented.
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