On the correlations of galaxy peculiar velocities and their covariance

Measurements of the peculiar velocities of large samples of galaxies enable new tests of the standard cosmological model, including determination of the growth rate of cosmic structure that encodes gravitational physics. With the size of such samples now approaching hundreds of thousands of galaxies, complex statistical analysis techniques and models are required to extract cosmological information. In this paper, we summarize how correlation functions between galaxy velocities, and with the surrounding large-scale structure, may be utilized to test cosmological models. We present new determinations of the analytical covariance between such correlation functions, which may be useful for cosmological likelihood analyses. The statistical model we use to determine these covariances includes the sample selection functions, observational noise, curved-sky effects, and redshift-space distortions. By comparing these covariance determinations with corresponding estimates from large suites of cosmological simulations, we demonstrate that these analytical models recover the key features of the covariance between different statistics and separations, and produce similar measurements of the growth rate of structure.