The velocity coherence scale R_v marks the onset of statistical homogeneity, is redshift-independent in comoving coordinates, and connects directly to the matter-radiation equality scale k_eq in standard cosmology.
The Peculiar Velocity Correlation Function
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abstract
We present an analysis of the two-point peculiar velocity correlation function using data from the CosmicFlows catalogues. The Millennium and MultiDark Planck 2 N-body simulations are used to estimate cosmic variance and uncertainties due to measurement errors. We compare the velocity correlation function to expectations from linear theory to constrain cosmological parameters. Using the maximum likelihood method, we find values of $\Omega_m= 0.315^{+0.205}_{-0.135}$ and $\sigma_8=0.92^{+0.440}_{-0.295}$, consistent with the Planck and Wilkinson Microwave Anisotropy Probe CMB derived estimates. However, we find that the cosmic variance of the correlation function is large and non-Gaussian distributed, making the peculiar velocity correlation function less than ideal as a probe of large-scale structure.
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The velocity coherence scale: a novel probe of cosmic homogeneity and a potential standard ruler
The velocity coherence scale R_v marks the onset of statistical homogeneity, is redshift-independent in comoving coordinates, and connects directly to the matter-radiation equality scale k_eq in standard cosmology.