28379 2509.25013 10.1007/JHEP03(2026)072 72 72 Gravitational waves from axion inflation in the gradient expansion formalism. Part II. Fermionic axion inflation Regular Article - Theoretical Physics 1 35 2026 3 9 2025 10 9 2025 11 20 2025 12 16 2026 3 9 2026 3 9 The Author(s) 2026 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2026 2026 3 3 Richard von Eckardstein richard.voneckardstein@uni-muenster.de Kai Schmitz kai.schmitz@uni-muenster.de Oleksandr Sobol oleksandr.sobol@uni-muenster.de https://ror.org/00pd74e08 grid.5949.1 0000 0001 2172 9288 Institute for Theoretical Physics University of Münster Wilhelm-Klemm-Straße 9 48149 Münster Germany https://ror.org/057zh3y96 grid.26999.3d 0000 0001 2169 1048 Kavli IPMU (WPI) UTIAS, The University of Tokyo 5-1-5 Kashiwanoha, Kashiwa Chiba 277-8583 Japan https://ror.org/02aaqv166 grid.34555.32 0000 0004 0385 8248 Physics Faculty Taras Shevchenko National University of Kyiv 64/13, Volodymyrska Street Kyiv 01601 Ukraine Abstract Axion inflation represents an intriguing source of gravitational waves (GWs) from the early Universe. In a companion paper [1], we previously leveraged the gradient expansion formalism (GEF) to investigate pure axion inflation (PAI), i.e., axion inflaton coupled to a pure gauge sector. In this paper, we extend our analysis to fermionic axion inflation (FAI), i.e., we allow for the presence of fermions in the gauge sector. PAI predicts a strongly blue-tilted GW spectrum; in our GEF benchmark study, all parameter regions leading to observable GWs turned out to violate the upper limit on the number of extra relativistic degrees of freedom, ∆N eff. As we demonstrate in this paper, the situation is different for FAI: Schwinger pair creation of the charged fermions results in a damping of gauge-field production, which attenuates the GW signal. As a result, the GW signal from FAI can fall into the sensitivity reach of LISA and ET without violating the upper limit on ∆N eff. This result notably applies to the arguably most realistic variant of Abelian axion inflation, in which the axion couples to the hypercharge sector of the Standard Model. Besides, we discuss GW emission from the fermion gas, which may further enhance the total GW signal but which also requires a more quantitative investigation in future work. Additionally, we identify a new backreaction regime in which fermion production moderates the axion-vector dynamics. In this regime, the axion velocity and all energy-density components exhibit oscillations analogous to the strong backreaction in PAI, but here, the oscillations occur around the slow-roll trajectory and are damped by the presence of charged fermions. These observations define again an interesting GEF benchmark for future lattice studies. Keywords Early Universe Particle Physics Cosmology of Theories BSM Axions and ALPs ArXiv ePrint: 2509.25013