Finite-duration non-slow-roll effects in inflationary production of ultralight vector dark matter

Inflationary production of ultralight vector dark matter can be amplified by a brief non-slow-roll phase, yet instantaneous mass transitions generate ultraviolet ringing and leave finite-time predictions unresolved. We replace the sharp transition with a smooth profile and derive the momentum-response kernel of the longitudinal mode. Finite duration preserves the infrared enhancement, suppresses modes that resolve the transition, and introduces a profile-dependent correction to the relic abundance. After fixing the dark matter abundance, the induced gravitational-wave signal retains an independent transverse-traceless source dependence, so abundance rescaling alone leaves residual profile information. Numerical mode evolution and radiation-era tensor integration support the finite-width treatment. Transition duration therefore links microscopic inflationary dynamics to ultralight vector abundance and its low-frequency gravitational-wave signal.

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