Probing Time-Dependent Physics with Phase-Folding CMB Maps

Abstract

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.

Figures (7)

• Figure 1: The left panel shows the lensing potential $\psi$ used in the toy model on a $10^\circ \times 10^\circ$ patch. The white arrows illustrate the direction and relative size of $\star\nabla \psi$ (scaled for visualization). The right panel illustrates the effect of a 10 Hz gravitational background to the effective scan path. The black dashed curve illustrates the undeflected scan pattern; the red curves illustrates the deflected scan pattern due to lensing effect from the 10 Hz gravitational wave. While all pixels are scanned across in an observation, we only show selected scan paths for illustration. The effect of deflection has been enlarged by 50 times in this visualization. The background shows the primary CMB field.
• Figure 2: Illustration of the phase-folding mapmaking output for the toy model. Left: The input, unlensed CMB temperature anisotropy map on the $8^\circ \times 8^\circ$ patch. Middle: The average sky map, $\mathcal{M}(\hat{\mathbf{n}}, 0)$, constructed from all data, showing the standard CMB. The effect of the time-dependent lensing causes a blurry effect when exaggerated by 50 times for visualization purpose. Right: The oscillating mode map, $\mathcal{M}(\hat{\mathbf{n}}, 1)$, which isolates the signal modulated at the GW frequency. The clear, non-random spatial pattern is indicative of a coherent signal.
• Figure 3: Demonstration of the phase-resolved lensing reconstruction in a toy model. Left: The input curl potential $\psi(\hat{\mathbf{n}})$ (a pure $l=2, m=2$ mode) used to generate the time-dependent deflection. Middle: The reconstructed curl potential $\hat{\psi}(\hat{\mathbf{n}})$ recovered by applying the quadratic estimator (Eq. \ref{['eq:gen_estimator']}) to the simulated data. Right: The residual difference map, $\psi - \hat{\psi}$, which is consistent with instrumental noise. The successful recovery of the input signal validates the formalism.
• Figure 4: Forecasted sensitivity to the characteristic strain $h_c(f)$ of a stochastic gravitational wave background. The red curve shows the projected reach of the phase-folding CMB method with SO LAT-like experiment with $\Delta_T=1\,\mu \mathrm{K}'$, $f_{\text{sky}}=0.5$, $N_b=10$, integrated over 10 years with a 200 Hz sampling rate. We compare against sensitivity curves from pulsar timing arrays (NANOGrav 15 year, green), space-based interferometers (LISA, blue, and ground-based detectors (Advanced LIGO, orange).
• Figure 5: This diagram illustrates of the effect of a 45$^\circ$ time-dependent polarization rotation oscillating at around 1.2 Hz on the detector polarization response at various points in a scan. The black solid lines show the unrotated detector polarization response, which is a constant on the sky for illustration. The red lines show the effective detector polarization response caused by time-dependent polarization rotations. While the scan covers every pixel in the map, we only show selected paths for illustration. The background shows the primary CMB field.