Primordial Black Hole Seeds for Little Red Dots in $f(R)$ Gravity

Saeed Fakhry

First listed 2026-09-01 | Last updated 2026-09-01

Abstract

Short digest

Fakhry presents a hybrid early-black-hole assembly scenario in which clustered primordial black holes undergo hierarchical gravitational-wave-capture mergers in Hu–Sawicki f(R) gravity before their remnants grow through galactic gas accretion. The screened fifth force boosts the early merger kernel and hence the intermediate-mass seed population, while chameleon screening regulates the enhancement; because later accretion scales with seed mass, the model lowers the time-averaged Eddington ratios needed to reach little-red-dot black-hole masses by z≈6. The predicted active mass functions can reproduce the reported LRD space densities with a small clustered PBH fraction and an AGN duty cycle of 10^-2, while the paper proposes remnant-spin states, an SGWB cutoff, and a scale-dependent PBH-clustering inversion as ways to distinguish modified gravity from denser PBH clusters.

Key figures to inspect

• Figure 1. This establishes the central assembly claim directly: Hu–Sawicki gravity raises the maximum black-hole mass relative to GR during the merger-plus-accretion epoch, reducing the Eddington ratio needed to enter the observed LRD mass range by z≈6.
• Figure 5. This is the main population-level test of the model, comparing active black-hole mass functions at z≈5.5 and z≈6.5 against LRD mass-distribution information and other observational constraints while varying PBH fraction and f(R) strength.
• Figure 6. This figure presents one of the paper’s proposed degeneracy-breaking observables: the stochastic gravitational-wave background and its observer-frame ISCO cutoff, which encode the merger-built PBH seed population.
• Figure 8. This captures the other distinctive large-scale diagnostic emphasized by the paper, showing how the PBH real-space correlation function at z=6 differs between GR and screened f(R) models.