Probing Time-Dependent Physics with Phase-Folding CMB Maps

Time-resolved observations of the Cosmic Microwave Background (CMB) offer a powerful probe of time-dependent cosmological signals, such as a stochastic gravitational wave background passing through Earth, which imprints a time-varying deflection on the CMB, and time-dependent cosmic birefringence, which induces an oscillating polarization rotation. However, analyses based on time-division CMB maps are fundamentally limited by the mapmaking cadence, restricting sensitivity to frequencies below $\sim 10^{-5}$ Hz. In this paper we develop a phase-folding mapmaking framework to enable targeted searches of such periodic cosmological signals with frequencies up to the detector sampling rate of $O(100)$ Hz. We demonstrate the power of this framework with two cosmological applications: (1) constraining a stochastic gravitational wave background via its time-dependent lensing signature, and (2) the search for an oscillating polarization rotation from axion-like particles. We show that this technique transforms CMB experiments into broadband probes of the oscillating sky, extending their constraining power from the microhertz regime up to $O(100)$ Hz-an expansion of over seven orders of magnitude in frequency. This provides a new observational window, complementary to other approaches by probing under-explored frequency ranges for gravitational waves and axion-like particles.