Gauge-field energy density in inflationary kinetic-coupling models: QFT regularization versus horizon cutoffs
Coupling gauge fields to the inflaton can amplify their quantum fluctuations during inflation, with potential applications to a range of cosmological phenomena. A central challenge is to define finite and physically meaningful observables, such as the gauge-field energy density. In this work, we study an Abelian gauge field kinetically coupled to the inflaton through $f^2(ϕ)F_{μν}F^{μν}$ in a de Sitter background with $f\propto a^{γ_1}$, and compare conventional quantum-field-theoretic regularization with horizon-cutoff prescriptions. Using a hard physical-momentum cutoff and dimensional regularization, we derive the ultraviolet divergences in closed form and fix the remaining one-parameter finite-part ambiguity by requiring the coupling-induced total energy density to be nonnegative. We then examine five horizon-cutoff prescriptions based on characteristic scales of the mode equations. Their predictions depend sensitively on the choice of horizon scale and, for weak gauge-field production, can deviate substantially from the regularized result; for the adopted finite-part prescription, the minimal horizon agrees best with the regularized total energy density. As $|γ_1|\to 2$, where infrared modes dominate, the relative deviation of all prescriptions from the regularized result vanishes, independently of the finite-part prescription. Outside this regime, the separate electric and magnetic contributions, which can become negative after regularization, are not reliably reproduced by any of the horizon-cutoff prescriptions.