Abstract
The apparent distribution of large-scale structures in the universe is sensitive to the velocity/potential of the sources as well as the potential along the line-of-sight through the mapping from real space to redshift space (redshift-space distortions, RSD). Since odd multipoles of the halo cross-correlation function vanish when considering standard Doppler RSD, the dipole is a sensitive probe of relativistic and wide-angle effects. We build a catalogue of ten million haloes (Milky-Way size to galaxy-cluster size) from the full-sky light-cone of a new "RayGalGroupSims" N-body simulation which covers a volume of ($2.625~h^{-1}$Gpc)$^3$ with $4096^3$ particles. Using ray-tracing techniques, we find the null geodesics connecting all the sources to the observer. We then self-consistently derive all the relativistic contributions (in the weak-field approximation) to RSD: Doppler, transverse Doppler, gravitational, lensing and integrated Sachs-Wolfe. It allows us, for the first time, to disentangle all contributions to the dipole from linear to non-linear scales. At large scale, we recover the linear predictions dominated by a contribution from the divergence of neighbouring line-of-sights. While the linear theory remains a reasonable approximation of the velocity contribution to the dipole at non-linear scales it fails to reproduce the potential contribution below $30-60~h^{-1}$Mpc (depending on the halo mass). At scales smaller than $\sim 10~h^{-1}$Mpc, the dipole is dominated by the asymmetry caused by the gravitational redshift. The transition between the two regimes is mass dependent as well. We also identify a new non-trivial contribution from the non-linear coupling between potential and velocity terms.
Highlights
Late time structure formation is a non-linear process which is very sensitive to the underlying cosmology
Nonlinear effects are already visible in real space at 100 h−1Mpc scales in Baryon Acoustic Oscillations (BAO) (Crocce & Scoccimarro 2008; Taruya et al 2012; Rasera et al 2014)
The first part is the one generated by statistical fluctuations in real space
Summary
Late time structure formation is a non-linear process which is very sensitive to the underlying cosmology. We do not observe large-scale structures in themselves but rather an image of these objects via messengers (photons, neutrinos, gravitational waves, etc.). Most of our observations come from light, but the information transported by photons is altered during their path from the source to the observer. This leads to several distortions of the image and linear theory does not provide a fully satisfactory prediction since small scales are dominated by nonlinear clustering and large-scale modes can be affected by smaller scale modes through mode coupling. One important limitation of most of these works is that only standard RSD have been considered (distant-observer approximation and no relativistic effects)
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