Redshift-space distortions with split densities

Accurate modelling of redshift-space distortions (RSD) is challenging in the non-linear regime for two-point statistics e.g. the two-point correlation function (2PCF). We take a different perspective to split the galaxy density field according to the local density, and cross-correlate those densities with the entire galaxy field. Using mock galaxies, we demonstrate that combining a series of cross-correlation functions (CCFs) offers improvements over the 2PCF as follows: (1) The distribution of peculiar velocities in each split density is nearly Gaussian. This allows the Gaussian streaming model for RSD to perform accurately within the statistical errors of a (1.5 h(-1) Gpc)(3) volume for almost all scales and all split densities. (2) The probability distribution of the density contrast at small scales is non-Gaussian, but the CCFs of split densities capture the non-Gaussianity, leading to improved cosmological constraints over the 2PCF. We can obtain unbiased constraints on the growth parameter f sigma(12) at the per cent level, and Alcock-Paczynski (AP) parameters at the sub-per cent level with the minimal scale of 15 h(-1)Mpc. This is a similar to 30 per cent and similar to 6 times improvement over the 2PCF, respectively. The diverse and steep slopes of the CCFs at small scales are likely to be responsible for the improved constraints of AP parameters. (3) Baryon acoustic oscillations (BAO) are contained in all CCFs of split densities. Including BAO scales helps to break the degeneracy between the line-of-sight and transverse AP parameters, allowing independent constraints on them. We discuss and compare models for RSD around spherical densities.

Automated summary

This study takes a different perspective by splitting the galaxy density field and using cross-correlation functions to accurately model redshift-space distortions. Compared to the conventional two-point correlation function method, this approach provides more accurate cosmological constraints at various scales and improves the applicability of the model by including BAO scales.