Constraining cosmological vorticity modes with CMB secondary anisotropies

Observational searches for large-scale vorticity modes in the late time Universe are underexplored. Within the standard $\Lambda$CDM model, this is well motivated given the observed properties of the cosmic microwave background (CMB). However, this means that searches for cosmic vorticity modes can serve as a powerful consistency test of our cosmological model. We show that through combining CMB measurements of the kinetic Sunyaev-Zel'dovich and the moving lens effects with galaxy survey data we can constrain vorticity fields independently from the large scale cosmic velocity field. This approach can provide stringent constraints on the largest scale modes and can be achieved by a simple change in the standard estimators. Alternatively if one assumes there are no cosmic vorticity modes, this estimator can be used to test for systematic biases in existing analyses of kinetic Sunyaev-Zel'dovich effect in a manner analogous to curl-lensing.