Redshift-space distortions, pairwise velocities, and nonlinearities

Abstract

We derive the exact relationship, including all non-linearities, between real-space and redshiftspace two-point statistics through the pairwise velocity distribution function. We show using numerical simulations that the pairwise velocity PDF is strongly non-Gaussian at all scales, and explain why this is so. We caution that a commonly used ansatz to model the redshift-space power spectrum gives rise to an unphysical distribution of pairwise velocities, and show that it is in general impossible to derive the distribution from measurements of redshift-space clustering. Methods that claim to do this obtain instead something else, whose properties we derive.We provide a general derivation of the large-scale limit of the redshift-space power spectrum and show that it differs from the Kaiser formula by terms that depend on Gaussian and nonGaussian contributions to the velocity dispersion of large-scale flows. We also show that the large-scale evolution of velocity fields is not well described by linear theory and discuss how this impacts the redshift-space power spectrum. Finally, we stress that using the monopole of the redshift-space power as an indicator of the real-space power spectrum shape can lead to systematic effects in the determination of cosmological parameters; nevertheless a simple procedure is able to recover the large-scale real-space power spectrum rather well.

Simulations of Dark Energy Cosmologies

“…In this chapter, we focus on the impact of non-linearities and determine their impact on the redshift space power spectrum in ΛCDM and quintessence dark energy models. The volume of our simulations, detailed in Chapters 2 and 3, is 125 times larger than that used by Cole et al (1994) and approximately 27 times larger than the one used by Scoccimarro (2004), and allow us to accurately predict the redshift space distortions for each cosmology out to very large scales.…”

“…4.8, the term in square brackets can be re-written in terms of these non-linear velocity divergence power spectra by multiplying out the brackets and using the fact that µ i = k i ·ẑ/k i . Scoccimarro (2004) proposed the following model for the redshift space power spectrum in terms of P δ δ , the non-linear matter power spectrum, P θ θ and P δ θ ,…”

“…Kaiser, 1987). Scoccimarro (2004) extended the analysis of Kaiser (1987) into the non-linear regime, including the contribution of peculiar velocities on small scales. We study the distortions in the redshift space power spectrum in ΛCDM and quintessence dark energy models, using large volume N-body simulations, and test predictions for the form of the redshift space distortions.…”

“…These previous studies do not provide an accurate description of the non-linearities in the velocity field as the Zel'dovich approximation does not model the velocities correctly, as it only treats part of the bulk motions, and in a computational box of length 300h −1 Mpc, the power which determines the bulk flows has not converged. Scoccimarro (2004) measured the large scale form of the redshift space power spectrum using the VLS simulation of the Virgo consortium in a box of length 479 h −1 Mpc , and found discrepancies from the Kaiser formula on scales k > 0.1hMpc −1 . Assuming a ΛCDM cosmology, Scoccimarro (2004) also found significant non-linear corrections due to the evolution of the velocity fields on large scales.…”

“…Scoccimarro (2004) measured the large scale form of the redshift space power spectrum using the VLS simulation of the Virgo consortium in a box of length 479 h −1 Mpc , and found discrepancies from the Kaiser formula on scales k > 0.1hMpc −1 . Assuming a ΛCDM cosmology, Scoccimarro (2004) also found significant non-linear corrections due to the evolution of the velocity fields on large scales. In this chapter, we focus on the impact of non-linearities and determine their impact on the redshift space power spectrum in ΛCDM and quintessence dark energy models.…”