Probing the Seed Effect of Supermassive Primordial Black Holes with Weak Gravitational Lensing

We investigate the cosmological implications of supermassive primordial black holes (PBHs) as a component of dark matter (DM), focusing on their seed effect on large-scale structure formation. In contrast to the Poisson effect associated with the discrete distribution of PBHs, the seed effect arises because PBHs act as early gravitational seeds, accreting surrounding DM and developing dense DM spikes to form dressed PBHs. These structures enhance the matter power spectrum, particularly on small scales. We model their contribution within the halo-model framework under two prescriptions for DM accretion: an optimistic scenario (Case 1) and a conservative scenario (Case 2), which predict different modifications to the 1-halo term. We constrain the PBH abundance using weak-lensing measurements from the Dark Energy Survey Year 3 (DES Y3), performing a Markov Chain Monte Carlo analysis to derive upper limits on the PBH fraction fPBH, as a function of the PBH mass MPBH. We find that weak lensing places competitive constraints on supermassive PBHs, with the upper limits on fPBH becoming progressively stronger toward higher PBH masses. Case 1, which predicts more efficient DM accretion and hence a larger enhancement of the matter power spectrum, yields stronger constraints than Case 2; in particular, it excludes fPBH10⁻⁴ for MPBH10¹⁰ M_. We further forecast the sensitivity of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) using mock weak-lensing data and find that the constraints could improve by approximately two orders of magnitude. Our results establish weak gravitational lensing as a sensitive probe of the seed effect of supermassive PBHs and demonstrate its potential to complement other cosmological and astrophysical searches.