A new method of measuring the peculiar velocity power spectrum

We show that by directly correlating the cluster kinetic Sunyaev Zeldovich (KSZ) flux, the cluster peculiar velocity power spectrum can be measured to $\sim 10$ accuracy by future large sky coverage KSZ surveys. This method is almost free of systemics entangled in the usual velocity inversion method. The direct correlation brings extra information of density and velocity clustering. We utilize these information to construct two indicators of the Hubble constant and comoving angular distance and propose a novel method to constrain cosmology.