This paper shows a simple way to make lots of very heavy particles while the Universe is inflating. The idea uses two ingredients: a small term that breaks the usual particle–antiparticle symmetry for a complex field, and a derivative coupling between the inflaton (the field driving inflation) and the particle’s U(1) current. Together these create an effective “chemical potential” that drives resonant particle production even when the particle mass is larger than the Hubble scale during inflation.

The authors model the produced species as a complex scalar field χ charged under a global U(1). A dimension‑five coupling of the form ∂µϕ Jµ (where ϕ is the inflaton and Jµ the U(1) current) gives an effective chemical potential µ = ˙ϕ0/Λ. A quadratic U(1)-breaking mass term (proportional to χ2 + χ*2) mixes particles with antiparticles. After a time-dependent field rotation the breaking term appears as an oscillatory “pump” with frequency 2µ. This oscillation periodically violates adiabatic evolution and opens resonant windows. The resonance can produce χ quanta efficiently and avoids the usual exponential Boltzmann suppression e^{−πm/H} that makes gravitational production of very heavy particles otherwise negligible.

Large bursts of particle production change the stress in the early Universe. In quantum field language, big occupation numbers mean large field fluctuations and a sizable anisotropic stress. That stress sources tensor perturbations, i.e., a stochastic background of primordial gravitational waves (GWs). The paper computes the primordial tensor spectrum from these sourced tensor modes, and then maps it to the present-day energy density spectrum ΩGW(f). Because the source acts during inflation, redshifting can move the peak of the spectrum into observational bands. Depending on when the source is active and on the post‑inflation thermal history, the peak frequency can lie in the kilohertz, millihertz or nanohertz ranges. The authors compare their projected signals with sensitivities of ongoing and proposed detectors, from ground interferometers (LIGO/Virgo/KAGRA) to space missions (LISA, TianQin, Taiji) and pulsar timing arrays.