Redshift Drift in Relativistic N-Body Simulations

TL;DR

The study addresses how cosmic structures affect the directly observable redshift drift by performing fully relativistic N-body simulations with ray-tracing on light cones in a $\Lambda$CDM universe. It develops analytic perturbation-theory expressions for the drift and its angular power spectrum, and validates them against high-resolution simulations using the gevolution code for 10 observers. The results show that, except at very low redshift, the mean drift adheres closely to the FLRW background, while fluctuations can be as large as the signal at $z$ below about 0.15, driven by peculiar accelerations in clusters; the linear theory matches the simulations for linear scales, but a surprisingly large non-linear component appears at low multipoles. These findings imply that redshift drift measurements with SKA/ELT will predominantly constrain background expansion while also encoding velocity and acceleration field information, and that extreme outliers may enable novel cluster-potential probes.

Abstract

The cosmological redshift drift promises to be the first observable directly measuring the evolution of the cosmic expansion rate and should be detectable with upcoming surveys by the Square Kilometre Array and the Extremely Large Telescope. To prepare for these upcoming measurements we study the redshift drift in detail using the relativistic N-body code $\texttt{gevolution}$, focusing on inhomogeneity-induced fluctuations. Using a ray-tracer, we calculate the redshift drift directly from the light cone at two different time steps. To investigate observer-dependent biases we consider 10 different observers. We find that inhomogeneity-induced fluctuations in the redshift drift can in extreme cases be of the same order as the cosmic signal for $z\lesssim0.15$. By comparing our results to first-order perturbation theory, we find that the extreme outliers are due to peculiar motion in over-densities and can be described by first-order perturbation theory to percent precision. We calculate angular power spectra that fit very well with our predictions based on perturbation theory at linear scales and show a surprisingly large non-linear signal. This shows that redshift drift not only has the power to measure the background expansion, but could also deliver information about the velocity and acceleration fields in clusters.

Figures (12)

• Figure 1: Relative difference between the mean redshift drift in 40 bins and the expected FLRW background result plotted as a function of the redshift for 10 different observers.
• Figure 2: Normalized histograms of the relative fluctuations of the redshift drift around the background FLRW prediction in three different redshift bins $z=0.1,0.2,0.3\pm 0.01$ for 10 different observers.
• Figure 3: The redshift drift as a function of the redshift for observer 1 plotted as a hexbin density map.
• Figure 4: Left: Slice through the observed light cone with width $\mathrm{d} z = 0.01$. Shown are the number density of particles (grey), with those particles highlighted that have $|\delta z -\delta\bar{z}| > 0.8\times 10^{-10}$. Right: The same as left, but with those particles with $|\delta z -\delta\bar{z}| > 0.2\times 10^{-10}$ highlighted.
• Figure 5: HEALPix skymaps of the redshift drift fluctuations around the FLRW background prediction, for three different redshift bins $z=0.1,0.2,0.3\pm0.01$ and three different observers. The map for $z\sim 0.1$ shows the full sky with resolution $N_\mathrm{side}=256$, while the maps for $z\sim 0.2,0.3$ show partial circular sections of the sky from a pencil beam light cone with half-opening angle 25° and have a resolution $N_\mathrm{side}=512$. These figures are log-scaled between $10^{-10}$ and $10^{-11}$ and linearly scaled between $0$ and $10^{-11}$ to allow both visualization of outliers and the underlying distribution.