Time-dependent deflection reconstruction: new technique to search for gravitational waves with the cosmic microwave background

Abstract Gravitational waves (GWs) passing through the Earth cause a correlated pattern of time-dependent deflections of the apparent position of astronomical sources. We build upon standard lensing reconstruction techniques to develop a new time-dependent optimal quadratic estimator, providing a novel technique to search for the deflections produced by GWs using observations of the cosmic microwave background (CMB). We find that the time-dependent deflection reconstruction is many orders of magnitude more sensitive than the ordinary static lensing estimator, and that it can be employed with the data collected by existing and future CMB surveys, without requiring any modification to the experimental or survey design. We demonstrate that CMB surveys offer sensitivity to GWs across a broad frequency range: while the sensitivity will not be competitive over the frequency range covered by pulsar timing arrays, the coverage band extend to both lower and higher frequencies. Finally, we discuss how our methods can be adapted to search for other time-varying signals, and also how they can be applied to surveys at other wavelengths.