Minimal Magnetogenesis: The Role of Inflationary Perturbations and ALPs, and Its Gravitational Wave Signatures

Any attempt to understand the ubiquitous nature of the magnetic field in the present universe seems to lead us towards its primordial origin. For large-scale magnetic fields, however, their strength and length scale may not necessarily originate from a singular primordial mechanism, namely inflationary magnetogenesis, which has been a popular consideration in the literature. In this paper, we propose a minimal scenario wherein a large-scale magnetic field is generated from the inflationary perturbation without any non-conformal coupling. Due to their origin in the inflationary scalar spectrum, these primordial fields are inherently weak, with their strength suppressed by the small amplitude of scalar fluctuations. We then consider the coupling between this large-scale weak primordial magnetic field and a light axion of mass $<10^{-28}$ eV, which is assumed to be frozen in a misaligned state until the photon decoupling. After the decoupling, when the universe enters into a dark age, the light axion coherently oscillates. By appropriately tuning the axion-photon coupling parameter $\alpha$, we demonstrate that a large-scale magnetic field of sufficient strength can indeed be generated through tachyonic resonance. We further show that the produced magnetic field induces a unique spectrum with multiple peaks of secondary gravitational waves, which the upcoming CMB-S4 can probe through B-mode polarization. The strength can be sufficient enough to violate the PLANCK bound on tensor-to-scalar ratio $r \lesssim 0.036$. Such a violation leads to a constraint on $\alpha \lesssim 80$. With this limiting value of the coupling, we find that present-day magnetic field strength could be as high as $10^{-10}$ Gauss at Mpc scale, consistent with observation.