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Cross-correlation between the CMB and large-scale structure is a powerfulprobe of dark-energy and gravity on the largest physical scales. We introduce anovel estimator, the CMB-velocity correlation, that has most of his power onlarge scales and that, at low redshift, delivers up to factor of two highersignal-to-noise ratio than the recently detected CMB-dark matter densitycorrelation expected from the Integrated Sachs-Wolfe effect. We propose to usea combination of peculiar velocities measured from supernovae type Ia andkinetic Sunyaev-Zeldovich cluster surveys to reveal this signal and forecastdark-energy constraints that can be achieved with future surveys. We stressthat low redshift peculiar velocity measurements should be exploited withcomplementary deeper large-scale structure surveys for precision cosmology.Comment: Matches version accepted for publication in PRD (November 2007 issue

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