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Primordial black holes formation in inflationary $F(R)$ models with scalar fields

E. O. Pozdeeva, S. Yu. Vernov

TL;DR

The paper develops a two-field inflationary framework within $F(R,\chi)$ gravity by adding an induced-gravity term and a quartic scalar potential to an $F(R)$ baseline and mapping to a chiral two-field cosmological model in the Einstein frame via a conformal transformation. It analyzes exact evolution equations, slow-roll and ultra-slow-roll regimes, and demonstrates a two-stage inflation that can generate enhanced curvature perturbations leading to PBH formation; PBH masses are estimated with $M_{PBH} \simeq M_{Pl}^2/H_e \exp[2(N_e-N_*)]$. Numerical exploration shows ACT/DESI-consistent inflationary parameters, with $n_s \approx 0.974$ and $r \approx 0.012$–$0.016$, and PBH masses spanning $10^{-17}M_\odot$ to $10^{-12}M_\odot$, potentially addressing dark matter. The work provides a framework to unify inflation and PBH production within modified gravity, while remaining phenomenological and highlighting paths toward more realistic, particle-physics-based models.

Abstract

We construct $F(R)$ gravity models with scalar fields to describe cosmological inflation and formation of primordial black holes (PBHs). By adding the induced gravity term and the fourth-order polynomial potential for the scalar field to the known $F(R)$ gravity model, and using a conformal transformation of the metric, we obtain a two-field chiral cosmological model. For some values of the model parameters, we get that the inflationary parameters of this model are in good agreement with the observations of the cosmic microwave background radiation obtained by the Atacama Cosmology Telescope. The estimation of PBH masses suggests that PBHs could be dark matter candidates.

Primordial black holes formation in inflationary $F(R)$ models with scalar fields

TL;DR

The paper develops a two-field inflationary framework within gravity by adding an induced-gravity term and a quartic scalar potential to an baseline and mapping to a chiral two-field cosmological model in the Einstein frame via a conformal transformation. It analyzes exact evolution equations, slow-roll and ultra-slow-roll regimes, and demonstrates a two-stage inflation that can generate enhanced curvature perturbations leading to PBH formation; PBH masses are estimated with . Numerical exploration shows ACT/DESI-consistent inflationary parameters, with and –, and PBH masses spanning to , potentially addressing dark matter. The work provides a framework to unify inflation and PBH production within modified gravity, while remaining phenomenological and highlighting paths toward more realistic, particle-physics-based models.

Abstract

We construct gravity models with scalar fields to describe cosmological inflation and formation of primordial black holes (PBHs). By adding the induced gravity term and the fourth-order polynomial potential for the scalar field to the known gravity model, and using a conformal transformation of the metric, we obtain a two-field chiral cosmological model. For some values of the model parameters, we get that the inflationary parameters of this model are in good agreement with the observations of the cosmic microwave background radiation obtained by the Atacama Cosmology Telescope. The estimation of PBH masses suggests that PBHs could be dark matter candidates.

Paper Structure

This paper contains 10 sections, 36 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. $F(R,\chi)$ gravity models and two-field models
  3. Evolution equations and inflation
  4. Exact evolution equations
  5. Slow-roll and ultra-slow-roll regimes of inflation
  6. $F(R,\chi)$ inflationary model suitable for PBH formation
  7. $F(R)$ inflationary models
  8. Two-field CCM
  9. Inflation at different values of the model parameters
  10. Conclusions

Figures (3)

  • Figure 1: The Hubble function $H(N)$ (left), the fields $\phi(N)$ [a red curve] and $\chi(N)$ [a blue curve] (center), and the potential $V_E$ with a trajectory (left). The model parameters are given in (\ref{['modelparam']}).
  • Figure 2: The evolution of the slow-roll parameters $\epsilon(N)$ (left) and $\eta(N)$ (center and right) during inflation. The model parameters are given in (\ref{['modelparam']}).
  • Figure 3: The values of the inflationary parameters $n_s$ (left), $r$ (center), and $A_s$ (right). The model parameters are given in (\ref{['modelparam']}).