One Feature, Three Clocks: Phase-Locked Gravitational Waves, Primordial Black Holes, and Non-Gaussianity from Periodic Warm Inflation

Abstract

A shift-symmetric inflaton dissipating into a thermal bath couples to that bath periodically, so its friction oscillates as the field rolls. We follow what this does to warm inflation when a thermal channel opens midway through the rolling: the friction surges, and the curvature spectrum grows a sharp, log-periodically modulated peak at small scales while the CMB scales stay untouched. It saturates Primordial Black Holes (PBHs) formation in the asteroid-mass window, where the PBHs can make up an order-unity fraction of the dark matter, and it sources a scalar-induced gravitational-wave background in two bands at once -- a peak at $h^2\Omega_{\rm GW}\simeq10^{-8}$ near $3$~mHz for LISA, and a second band at $h^2\Omega_{\rm GW}\sim10^{-11}$ from deci-hertz to a hundred hertz, within reach of DECIGO and the Einstein Telescope, fed by the friction's continued growth toward smaller scales. And a separate-universe computation places its equilateral bispectrum a quarter cycle ahead of the power spectrum -- an offset fixed by the running of the spectrum and so robust to the equilateral-shape coefficient. The two GW bands carry the same underlying log-period and freeze-out phase to leading order, and the bispectrum is expected to share them: a modulation seen at two widely separated frequencies, plausibly accompanied by a $\pi/2$-shifted bispectrum, is not something a single-scale feature can fake. Because the feature is localized in the field, it imprints the same log-periodic structure on multiple observables, tying the gravitational-wave bands, black-hole mass, and bispectrum phase to a single underlying clock. We derive the freeze-out transfer function in closed form and use it to cap the first two harmonics at one quarter, and we show that the high-frequency band is itself bounded by PBHs overproduction, which turns it into a constraint on how far the friction can grow.