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

The discovery by the James Webb Space Telescope (JWST) of an abundant population of compact little red dots (LRDs) and supermassive black holes at high redshifts poses a severe timing challenge for standard Eddington-limited growth from stellar remnants. In this work, we present a unified hybrid assembly framework in which intermediate-mass seed black holes are formed via hierarchical primordial black hole (PBH) mergers within dense clusters in Hu-Sawicki f(R) gravity, followed by galactic gas accretion. We demonstrate that the screened f(R) fifth force nonlinearly accelerates early seed formation through a quadratic enhancement of the gravitational-wave radiation-capture kernel, while environmental chameleon screening dynamically self-regulates the growth. Because subsequent gas accretion scales multiplicatively with seed mass, the f(R) seed enhancement is preserved throughout the accretion history, drastically reducing the time-averaged Eddington ratios required to assemble 10 6-10 9,M LRDs by cosmic dawn. Confronting our active mass functions with JWST data reveals that a small clustered PBH fraction (f PBH 10-3) under a realistic active galactic nucleus duty cycle (δ about 10-2) naturally matches observed LRD space densities at z about 5.5-6.5 while remaining fully compliant with LIGO-Virgo-KAGRA limits, with modified gravity naturally driving the high-mass tail. Finally, we show that parameter degeneracies between modified gravity and cluster density can be cleanly broken by combining three multi-messenger diagnostics: remnant spin state signatures, a stochastic GW background cutoff, and a scale-dependent inversion in the PBH spatial correlation function.