Abstract
ABSTRACT 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 fσ12 at the per cent level, and Alcock–Paczynski (AP) parameters at the sub-per cent level with the minimal scale of $15\, h^{-1}{\rm Mpc}$. This is a ∼30 per cent and ∼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.
Highlights
In the modern era of cosmology, galaxy redshift surveys have granted us the information to achieve percent-level constraints on the parameters of our cosmological paradigm, the Λ cold dark matter (ΛCDM) model
The diverse and steep slopes of the cross-correlation functions (CCFs) at small scales are likely to be responsible for the improved constraints of AP parameters
We have presented a new method to analyse the signature of redshift-space distortions (RSD) in clustering measurements inferred from galaxy redshift surveys
Summary
In the modern era of cosmology, galaxy redshift surveys have granted us the information to achieve percent-level constraints on the parameters of our cosmological paradigm, the Λ cold dark matter (ΛCDM) model. Alternative approaches for overcoming the limitation of twopoint measurements include higher-order statistics, such as the three-point correlation function and the bispectrum (e.g. Sefusatti et al 2006; Gil-Marín et al 2012; Slepian & Eisenstein 2015, 2017) [and the streaming model has recently been generalised to three-point correlation function (Kuruvilla & Porciani 2020)], non-linear transformation to re-Gaussianise the density field (Neyrinck et al 2009, 2011; Neyrinck 2011; Wang et al 2011), density split statistics for weak lensing analysis (Gruen et al 2016, 2018; Friedrich et al 2018), counts-in-cells statistics (Szapudi & Pan 2004; Klypin et al 2018; Jamieson & Loverde 2020; Mandal & Nadkarni-Ghosh 2020), and using the concept of separate Universe to model density-dependent two-point statistics (Wagner et al 2015; Chiang et al 2015), which, in essence, corresponds to a three-point quantity These approaches usually provide complementary cosmological constraints by accessing information from the non-Gaussian field.
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