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Primordial Black Holes Formation from Particle Production during Inflation

Encieh Erfani

Abstract

We study the possibility that particle production during inflation can source the required power spectrum for dark matter (DM) primordial black holes (PBH) formation. We consider the scalar and the gauge quanta production in inflation models, where in the latter case, we focus in two sectors: inflaton coupled i) directly and ii) gravitationally to a $U(1)$ gauge field. We do not assume any specific potential for the inflaton field. Hence, in the gauge production case, in a model independent way we show that the non-production of DM PBHs puts stronger upper bound on the particle production parameter. Our analysis show that this bound is more stringent than the bounds from the bispectrum and the tensor-to-scalar ratio derived by gauge production in these models. In the scenario where the inflaton field coupled to a scalar field, we put an upper bound on the amplitude of the generated scalar power spectrum by non-production of PBHs. As a by-product we also show that the required scalar power spectrum for PBHs formation is lower when the density perturbations are non-Gaussian in comparison to the Gaussian density perturbations.

Primordial Black Holes Formation from Particle Production during Inflation

Abstract

We study the possibility that particle production during inflation can source the required power spectrum for dark matter (DM) primordial black holes (PBH) formation. We consider the scalar and the gauge quanta production in inflation models, where in the latter case, we focus in two sectors: inflaton coupled i) directly and ii) gravitationally to a gauge field. We do not assume any specific potential for the inflaton field. Hence, in the gauge production case, in a model independent way we show that the non-production of DM PBHs puts stronger upper bound on the particle production parameter. Our analysis show that this bound is more stringent than the bounds from the bispectrum and the tensor-to-scalar ratio derived by gauge production in these models. In the scenario where the inflaton field coupled to a scalar field, we put an upper bound on the amplitude of the generated scalar power spectrum by non-production of PBHs. As a by-product we also show that the required scalar power spectrum for PBHs formation is lower when the density perturbations are non-Gaussian in comparison to the Gaussian density perturbations.

Paper Structure

This paper contains 8 sections, 40 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Constraints from Dark Matter Primordial Black Holes
  3. Particle Production during Inflation Models
  4. Gauge Production
  5. Model I: Inflaton Coupled Directly to the Gauge Field
  6. Model II: Inflaton Coupled Gravitationally to the Gauge Field
  7. Scalar Production
  8. Summary and Conclusions

Figures (4)

  • Figure 1: Fraction of the energy density of the universe collapsing into PBHs as a function of the PBH mass for the threshold $\zeta_{\rm th} = 0.4135$. The solid (dashed) curve is for the Gaussian (non-Gaussian) probability distribution function. The horizontal dotted line indicates the abundance of DM PBHs, $f \sim 10^{-19}$.
  • Figure 2: The total curvature power spectrum, ${\mathcal{P}_{\zeta}}$ as a function of particle production parameter, $\xi$. The DM PBHs bound is the dotted line and the dashed line shows the constraint on the power spectrum from the CMB Planck-XX.
  • Figure 3: Predicted values for the tensor-to-scalar ratio, $r$ (left panel) and the equilateral ${f_{\rm NL,\,\zeta}^{\rm equil.}}$ parameter (right plot) as a function of $\xi$ near the end of inflation. In left panel, the dashed line is Planck 2015 Planck-XX upper bound $r < 0.10$. The dashed line in the right plot is the $68\,\%$ CL upper bound for ${f_{\rm NL,\,\zeta}^{\rm equil.}}$Planck-XVII.
  • Figure 4: Power spectrum of curvature perturbations in the absence (solid curve) and the presence (dashed curve) of resonant particle creation in the Planck observational range; i.e. $k_{H_0} \lesssim k \lesssim 1$ Mpc$^{-1}$. Resonant particle production produces a peak at $k_i = 0.01$ Mpc$^{-1}$.