Resonant production of heavy particles during inflation and its gravitational wave signature

TL;DR

This work studies resonant production of a heavy $U(1)$-charged spectator during inflation using a quadratic $U(1)$-breaking term together with a time-dependent chemical potential $\mu = \dot{\phi}_0/\Lambda$. The mechanism enables efficient non-thermal production even when the diagonal mass is large, and the produced quanta source a stochastic GW background whose primordial spectrum $P_h^{\rm prim}(k)$ is computed via Bogoliubov theory and Green’s-function methods, then mapped to present-day $\Omega_{\rm GW,0}(f)$ using standard transfer functions. A key feature is the link to a cosmological collider signal, as the same couplings imprint oscillatory non-Gaussianities in the curvature perturbations in the squeezed limit, providing a cross-check of the framework. The results indicate that, for realistic choices of parameters, the GW signal can fall within the sensitivity bands of current and planned detectors across multiple frequency ranges, and the CC signal offers an independent observational handle on the underlying particle content and interactions during inflation.

Abstract

We show that a quadratic $U(1)$-breaking term, together with an effective chemical potential induced by a dimension five derivative coupling between the inflaton and the $U(1)$ current, can drive efficient particle production during inflation even when the $U(1)$ field is heavier than the Hubble scale. Notably, the chemical potential enables efficient production even when the $U(1)$-breaking mass is smaller than the effective diagonal mass. We compute the gravitational wave signal generated by this mechanism during inflation, derive the primordial tensor spectrum, and map it to the present day energy density $Ω_{\mathrm GW}(f)$. Assuming the $U(1)$ field constitutes the dominant component of dark matter, this mapping fixes the characteristic frequency, which we compare with projected sensitivity curves of ongoing and proposed gravitational wave observatories. Finally, we argue that the same dynamics are accompanied by a cosmological collider signal, providing an independent cross validation of the framework.

Figures (6)

• Figure 1: The evolution of the real and imaginary part of the mode function with different momentum.
• Figure 2: Left panel: The evolution of the comoving phase space number density of various mode with momentum range from $p/H \in (1,7)$, where blue/red denote mode with large/small momentum. Right panel: The comoving phase space distribution at given comoving time $H\tau = -1$ and $H\tau = -0.5$. The rapid oscillation of $n_p$ is evident in this plot.
• Figure 3: Constraints on the $(\mu/H, A/H)$ and $(\mu/H, m/H)$ planes with $H\tau_i = -100$, where color indicates $\log_{10} f_\chi$. The solid black, solid white, and dashed curves mark the contours $f_\chi = 0.01,0.1,1$ respectively. The dot-dashed curve denote the contour where $A^2 = m^2 + \mu^2$.
• Figure 4: The shape of the gravitational wave energy density spectrum $\Omega_{\rm GW}h^2$ as a function of frequency $f$ scaled by the frequency $f_*$ of the reference mode.
• Figure 5: Gravitational wave energy density spectrum $\Omega_{\rm GW}h^2$ as a function of frequency $f$ for the benchmark points listed in Table \ref{['table:Benchmark']}. For reference, we overlay representative projected sensitivity curves of selected ongoing and planned gravitational wave observatories.