The origin of magnetic fields observed on both astrophysical and cosmological scales is a compelling problem that has the potential to shed light on the early Universe. We analytically investigate inflationary magnetogenesis in scenarios where a brief departure from slow-roll inflation—akin to mechanisms proposed for primordial black hole formation—leads to enhanced magnetic field generation with a growing power spectrum. Focusing on the Ratra model, we derive an analytic bound on the growth of the magnetic field power spectrum in this context, showing that the spectral index can reach $d\ln {\mathcal{P}}_B/d\ln k=4.75$ during the growth phase. This growth enables amplification from cosmic-microwave-background-safe large-scale amplitudes to values of astrophysical relevance. We further compute the stochastic gravitational wave background sourced by the resulting magnetic fields, incorporating their rich spectral features. Under suitable conditions, the induced signal exhibits a characteristic frequency dependence and amplitude within reach of future gravitational wave observatories, providing a distinctive signature of this mechanism and a specific class of templates for upcoming gravitational wave searches.

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• Gravitational waves
• Inflation
• Primordial magnetic fields