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 scale of homogeneity in the Las Campanas Redshift Survey
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abstract
We analyse the Las Campanas Redshift Survey using the integrated conditional density (or density of neighbors) in volume-limited subsamples up to unprecedented scales (200 Mpc/$h$) in order to determine without ambiguity the behavior of the density field. We find that the survey is well described by a fractal up to 20-30 Mpc/$h$, but flattens toward homogeneity at larger scales. Although the data are still insufficient to establish with high significance the expected homogeneous behavior, and therefore to rule out a fractal trend to larger scales, a fit with a CDM-like spectrum with high normalization well represents the data.
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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.