Multi-Messenger Probes of Primordial Magnetogenesis, PBH Dark Matter, and Induced Gravitational Waves

The origin of the large-scale magnetic fields permeating the Universe and the nature of dark matter are two of the most enduring open questions in modern cosmology. In this work, we investigate a unified early-universe scenario in which both phenomena arise naturally from a single primordial magnetogenesis mechanism. We show that the generation of primordial magnetic fields during the post-inflationary era not only provides seeds for the coherent magnetic fields observed today on cosmological scales, but also enhances curvature perturbations at intermediate wavelengths. These amplified perturbations become sufficiently large to trigger the formation of primordial black holes (PBHs), which can contribute substantially—if not dominantly—to the present dark-matter abundance. The same enhanced scalar fluctuations responsible for PBH formation inevitably induce a stochastic background of gravitational waves (GWs). We analyze the spectral features of this induced GW background and demonstrate that it carries a detailed imprint of the underlying magnetogenesis model and the expansion history of the Universe, particularly during non-standard reheating phases. By combining constraints from large-scale magnetic fields, PBH abundances, and induced GWs, we establish a powerful multi-messenger approach for probing the physics of the early Universe.
Furthermore, we highlight how upcoming and next-generation gravitational-wave detectors—such as LISA, DECIGO, BBO, and the SKA pulsar-timing array—can measure or tightly constrain the predicted GW signal. Such observations offer a unique opportunity to reconstruct the spectral behavior of the induced GWs and thereby uncover information about the reheating dynamics and the primordial magnetic field spectrum. Our results emphasize that jointly analyzing electromagnetic, gravitational-wave, and early-universe cosmological signatures provides an exceptionally sensitive pathway to uncovering the mechanisms that shaped cosmic magnetism and the origin of dark matter.