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Formation of intermediate-mass black holes as primordial black holes in the inflationary cosmology with running spectral index

Toshihiro Kawaguchi, Masahiro Kawasaki, Tsutomu Takayama, Masahide Yamaguchi, Jun'ichi Yokoyama

TL;DR

This work addresses the origin of ultraluminous X-ray sources (ULXs) by proposing that intermediate-mass black holes (IMBHs) originate as primordial black holes formed from a highly peaked curvature-perturbation spectrum. The authors construct a two-stage inflation model (smooth hybrid inflation followed by new inflation) in which parametric resonance during inflaton oscillations generates a strong peak in the perturbation spectrum, correlated with a large negative running $\alpha$ of the spectral index. They show that the resulting PBH mass can be around $M_{PBH} \sim 10^2 M_\odot$, with an abundance $\Omega_{IMBH} \sim 10^{-4.5}$ that can account for ULXs while respecting CMB constraints, though achieving the required amplitude depends on the inflaton decay rate $\Gamma$. The analysis connects the PBH mass to the cosmological parameters $(n,\alpha)$ via contour relations, and predicts that future CMB measurements of a substantial negative running would support this IMBH-PBH formation scenario and its relevance to ULXs.

Abstract

Formation of primordial black holes (PBHs) on astrophysical mass scales is a natural consequence of inflationary cosmology if the primordial perturbation spectrum has a large and negative running of the spectral index as observationally inferred today, because double inflation is required to explain it and fluctuations on some astrophysical scales are enhanced in the field oscillation regime in between. It is argued that PBHs thus produced can serve as intermediate-mass black holes (IMBHs) which act as the observed ultraluminous X-ray sources (ULXs) by choosing appropriate values of the model parameters in their natural ranges. Our scenario can be observationally tested in near future because the mass of PBHs is uniquely determined once we specify the values of the spectral index and its running on large scales.

Formation of intermediate-mass black holes as primordial black holes in the inflationary cosmology with running spectral index

TL;DR

This work addresses the origin of ultraluminous X-ray sources (ULXs) by proposing that intermediate-mass black holes (IMBHs) originate as primordial black holes formed from a highly peaked curvature-perturbation spectrum. The authors construct a two-stage inflation model (smooth hybrid inflation followed by new inflation) in which parametric resonance during inflaton oscillations generates a strong peak in the perturbation spectrum, correlated with a large negative running of the spectral index. They show that the resulting PBH mass can be around , with an abundance that can account for ULXs while respecting CMB constraints, though achieving the required amplitude depends on the inflaton decay rate . The analysis connects the PBH mass to the cosmological parameters via contour relations, and predicts that future CMB measurements of a substantial negative running would support this IMBH-PBH formation scenario and its relevance to ULXs.

Abstract

Formation of primordial black holes (PBHs) on astrophysical mass scales is a natural consequence of inflationary cosmology if the primordial perturbation spectrum has a large and negative running of the spectral index as observationally inferred today, because double inflation is required to explain it and fluctuations on some astrophysical scales are enhanced in the field oscillation regime in between. It is argued that PBHs thus produced can serve as intermediate-mass black holes (IMBHs) which act as the observed ultraluminous X-ray sources (ULXs) by choosing appropriate values of the model parameters in their natural ranges. Our scenario can be observationally tested in near future because the mass of PBHs is uniquely determined once we specify the values of the spectral index and its running on large scales.

Paper Structure

This paper contains 9 sections, 24 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Generation of peaked power spectrum of initial curvature perturbation via a double inflation model
  3. Smooth hybrid new inflation model
  4. Generation of strong fluctuation via the parametric resonance
  5. Spectrum of the curvature perturbation for the formation of IMBHs
  6. Formation of primordial black holes via collapse of overdense region
  7. Amount of IMBHs
  8. Spectral index and typical mass of PBHs
  9. Summary and discussion

Figures (4)

  • Figure 1: The spectrum leading to the formation of IMBHs from the smooth hybrid new inflation model.
  • Figure 2: The differential mass spectrum (\ref{['eq:massspec-pre']}) calculated for the spectrum shown in Fig.\ref{['fig:spectrum']}.
  • Figure 3: The relation between the abundance of IMBHs $\Omega_{\mathrm{IMBH}}$ and the decay rate $\Gamma$.
  • Figure 4: Contour-lines of the typical mass of PBHs on the $n$-$\alpha$ plane.