Probing the largest cosmological scales with the correlation between the cosmic microwave background and peculiar velocities

Cross correlation between the cosmic microwave background (CMB) and large-scale structure is a powerful probe of dark energy and gravity on the largest physical scales. We introduce a novel estimator, the CMB-velocity correlation, that has most of its power on large scales and that, at low redshift, delivers up to a factor of 2 higher signal-to-noise ratio than the recently detected CMB-dark matter density correlation expected from the integrated Sachs-Wolfe effect. We propose to use a combination of peculiar velocities measured from supernovae type Ia and kinetic Sunyaev-Zeldovich cluster surveys to reveal this signal and forecast dark energy constraints that can be achieved with future surveys. We stress that low redshift peculiar velocity measurements should be exploited with complementary deeper large-scale structure surveys for precision cosmology.