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arxiv: 2509.21220 · v2 · submitted 2025-09-25 · 🌀 gr-qc · astro-ph.CO· hep-th

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

E.O. Pozdeeva , S.Yu. Vernov This is my paper

Pith reviewed 2026-05-18 13:53 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords F(R) gravityprimordial black holesinflationscalar fieldsdark matterconformal transformationcosmic microwave background
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0 comments X

The pith

Adding an induced gravity term and a polynomial potential to F(R) gravity yields a two-field model that fits observed inflation and allows primordial black holes to serve as dark matter.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors extend known F(R) gravity by incorporating an induced gravity term and a fourth-order polynomial potential for an additional scalar field. A conformal transformation then converts the system into a two-field chiral cosmological model. Specific parameter choices make the slow-roll inflation parameters consistent with cosmic microwave background data from the Atacama Cosmology Telescope. Estimates of the masses of primordial black holes formed in this setup fall in a range where they could constitute the dark matter. The construction demonstrates how gravitational modifications can link early-universe inflation to later dark matter phenomenology through black hole production.

Core claim

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.

What carries the argument

The two-field chiral cosmological model obtained via conformal transformation from the F(R) gravity with added induced gravity term and fourth-order polynomial potential.

If this is right

  • The inflationary parameters match Atacama Cosmology Telescope observations for appropriate model parameters.
  • Primordial black holes formed in the model have masses that position them as possible dark matter candidates.
  • The two-field dynamics remain stable for the selected parameter values without requiring additional exclusions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar modifications might be applied to other F(R) models to explore additional cosmological signatures.
  • This framework could be tested by checking consistency with large-scale structure formation data.
  • Variations in the polynomial coefficients might yield different PBH mass spectra for comparison with microlensing observations.

Load-bearing premise

The specific numerical values for the induced-gravity coefficient and the polynomial potential coefficients lead to stable two-field dynamics where slow-roll parameters and PBH abundance can be computed without instabilities or post-hoc adjustments.

What would settle it

A detailed computation revealing that the slow-roll parameters deviate significantly from Atacama Cosmology Telescope data or that the predicted PBH abundance is insufficient to explain dark matter would disprove the viability for these parameters.

Figures

Figures reproduced from arXiv: 2509.21220 by E.O. Pozdeeva, S.Yu. Vernov.

Figure 1
Figure 1. Figure 1: FIG. 1. The Hubble function [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The evolution of the slow-roll parameters [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The values of the inflationary parameters [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript constructs F(R) gravity models augmented by scalar fields, adding an induced-gravity term and a fourth-order polynomial potential to a known F(R) model. A conformal transformation yields a two-field chiral cosmological model. For selected numerical values of the free parameters, the inflationary observables are stated to agree with Atacama Cosmology Telescope data, and PBH mass estimates are given that suggest PBHs as dark-matter candidates.

Significance. A verified, stable two-field realization that simultaneously satisfies ACT constraints and produces a calculable PBH abundance would be a useful addition to the literature on PBH formation in modified gravity. The present manuscript supplies no such verification, so the significance remains prospective rather than demonstrated.

major comments (2)
  1. [two-field chiral model derivation] The central claim rests on the assertion that the chosen numerical values of the induced-gravity coefficient and the polynomial coefficients produce a stable two-field dynamics. No explicit check is supplied that the kinetic metric remains positive-definite or that the effective mass matrix is free of tachyonic modes along the inflationary trajectory (see the section deriving the two-field chiral model after conformal transformation). Without this check the reported slow-roll parameters and PBH spectrum cannot be regarded as reliable.
  2. [inflationary parameters and PBH mass estimation] The statement that inflationary parameters agree with ACT data for 'some values' of the model parameters is presented without the specific numerical values, the resulting slow-roll indices, or a direct comparison table or figure. Because the same parameters are subsequently used to estimate PBH masses, the procedure risks circularity: the parameters are adjusted to fit the CMB data and the PBH abundance is then read off from the same fit.
minor comments (2)
  1. [abstract] The abstract should specify the numerical ranges or example values of the induced-gravity coefficient and the polynomial coefficients that produce the reported agreement.
  2. [model construction] Notation for the two-field kinetic metric and the effective potential after conformal transformation should be introduced with explicit definitions before the numerical results are discussed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and indicate the changes we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: The central claim rests on the assertion that the chosen numerical values of the induced-gravity coefficient and the polynomial coefficients produce a stable two-field dynamics. No explicit check is supplied that the kinetic metric remains positive-definite or that the effective mass matrix is free of tachyonic modes along the inflationary trajectory (see the section deriving the two-field chiral model after conformal transformation). Without this check the reported slow-roll parameters and PBH spectrum cannot be regarded as reliable.

    Authors: We agree that an explicit stability analysis is necessary to support the reliability of the slow-roll parameters and PBH estimates. The original manuscript derives the two-field chiral model via conformal transformation but does not include a dedicated check of the kinetic metric signature or the mass-matrix eigenvalues. In the revised version we will add this analysis for the specific parameter choices used, demonstrating that the kinetic metric remains positive definite and that no tachyonic modes appear along the inflationary trajectory. revision: yes

  2. Referee: The statement that inflationary parameters agree with ACT data for 'some values' of the model parameters is presented without the specific numerical values, the resulting slow-roll indices, or a direct comparison table or figure. Because the same parameters are subsequently used to estimate PBH masses, the procedure risks circularity: the parameters are adjusted to fit the CMB data and the PBH abundance is then read off from the same fit.

    Authors: We acknowledge that the manuscript states agreement for selected parameter values without tabulating the explicit numbers or slow-roll indices. We will add a table listing the chosen values of the induced-gravity coefficient and polynomial coefficients, the resulting slow-roll parameters, and a direct comparison with ACT constraints. On the question of circularity, the parameters are fixed once by the requirement that the model reproduces the observed CMB spectrum; the PBH mass range is then obtained as a derived consequence of the same potential and perturbation spectrum. This is the standard procedure in the PBH literature, but we will clarify the logical separation of the two steps in the revised text. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard model-building with external benchmarks

full rationale

The paper starts from a known F(R) model, adds an induced-gravity term and fourth-order polynomial potential, performs a conformal transformation to a two-field chiral model, selects specific numerical parameter values, and reports that the resulting slow-roll parameters agree with ACT data while PBH masses fall in a range allowing dark-matter candidacy. This sequence is ordinary parameter tuning to match external observations followed by derived implications; the agreement is explicitly conditioned on chosen values rather than presented as an independent first-principles prediction. No quoted equation or step reduces the output to the input by construction, no self-citation is shown to be load-bearing for a uniqueness claim, and the comparison to ACT data supplies an external benchmark. The derivation therefore remains self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on a known F(R) base model plus two added terms whose coefficients are adjusted to data; no new entities are postulated and no machine-checked derivations are supplied.

free parameters (1)
  • induced gravity coefficient and polynomial coefficients
    Chosen so that the resulting slow-roll parameters match ACT observations
axioms (1)
  • domain assumption The base F(R) model is already viable and the conformal transformation preserves the required cosmological dynamics
    Invoked when the authors state they start from a known F(R) model and obtain a two-field chiral model

pith-pipeline@v0.9.0 · 5638 in / 1308 out tokens · 43288 ms · 2026-05-18T13:53:48.000678+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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Reference graph

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