We introduce a simple linear equation relating the line-of-sight peculiar velocity and density contrast correlation functions .
The relation , which we call the Gaussian cell two-point “ energy-like ” equation , is valid in the distant-observer-limit and requires Gaussian smoothed fields .
In the variance case , i.e . , at zero lag , the equation is similar in its mathematical form to the Layzer-Irvine cosmic energy equation . \beta estimation with this equation from the PSC z redshift galaxy survey and the SEcat catalogue of peculiar velocities is carried out , returning a value of \beta = 0.44 \pm 0.08 .
The applicability of the method for the 6dF galaxy redshift and peculiar motions survey is demonstrated with mock data where it is shown that beta could be determined with \approx 5 \% accuracy .
The prospects for constraining the dark energy equation of state with this method from the kinematic and thermal Sunyaev-Zel ’ dovich cluster surveys are discussed .
The equation is also used to construct a nonparametric mass density power spectrum estimator from peculiar velocity data .