Gravitational waves from axion inflation in the gradient expansion formalism II: Fermionic axion inflation

Abstract: Axion inflation represents an intriguing source of gravitational waves (GWs) from the early Universe. In a companion paper arXiv:2508.00798, 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, $\Delta N_{\rm eff}$. As we demonstrate in this paper, the situation is different for FAI: Schwinger pair creation of the charged fermions results in a damping of the 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 $\Delta N_{\rm eff}$. 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.