Probing the Largest Cosmological Scales with the CMB-Velocity Correlation

Cross-correlation between the 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 his power on large scales and that, at low redshift, delivers up to factor of two 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.