Transverse Velocities in Real-Time Cosmology: Position Drift in Relativistic N-Body Simulations

TL;DR

This work investigates position drift as a real-time observable of the transverse velocity field in cosmology, employing fully relativistic N-body simulations with gevolution and past-light-cone ray tracing. It shows that at linear order the drift scales with the transverse velocity via $\frac{d \mathbf{e}}{dt} \approx \frac{\mathbf{v}_\perp}{r}$, with non-linearities introducing about a $5\%$ deviation, and decomposes the signal into E- and B-modes to reveal that E-dominates on large scales while B grows on small, non-linear scales due to vorticity. The study links the angular spectra to velocity-field components, finds light-cone inhomogeneities bias the dipole but are unlikely to explain Gaia DR3’s redshift-dependent dipole, and provides a robust framework for interpreting future position-drift measurements from Gaia-like and VLBI/ngVLA-like surveys. Overall, it establishes the viability of position drift as a direct probe of the cosmological transverse velocity field and quantifies non-linear and observational biases in a fully relativistic setting.

Abstract

The era of real-time cosmology has begun. It is now possible to directly measure the apparent drift of high-redshift astronomical sources across the sky $\textit{in real time}$. This so-called $\textit{position drift}$ provides a valuable probe of the peculiar velocity field and cosmic structure formation by giving direct access to the transverse velocity, which is notoriously difficult to measure and is typically inferred statistically from the density field in a model-dependent way. To fully exploit this new window into the Universe, it is essential to understand how cosmological structures affect position drift measurements. Here we present the first position drift study based on the general relativistic N-body simulation code $\texttt{gevolution}$. We calculate the position drift directly from the past light cone for ten different observers and compare the results to predictions from linear perturbation theory. At linear order, the position drift is directly proportional to the transverse velocity on the sky. This linear approximation reproduces our non-linear simulation results to within about 5%. We calculate power spectra for the position drift, splitting the signal into an E- and B-mode and compare the former to linear expectations, finding good agreement. The B-mode is suppressed on linear scales, but has similar amplitude as the E-mode on non-linear scales. We further demonstrate that light-cone inhomogeneities induce biases in the dipole of the drift, introducing redshift dependence of both the amplitude and direction. Although our analysis is not yet sufficient for a firm conclusion, our results suggest that these effects alone cannot explain the possible redshift-dependent dipole in Gaia DR3 data reported in the literature.

Figures (9)

• Figure 1: HEALPix skymaps of the position drift, 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 $N_\mathrm{side}=16$, 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 $25^\circ$ and have a resolution $N_\mathrm{side}=64$. The colour of the vectors indicates the absolute value of the position drift. The highest density regions are indicated in grey in the background, visible upon zooming in.
• Figure 2: Absolute value of the mean (left), mean of the absolute value (centre), and standard deviation of the absolute value (right) of the position drift averaged in 40 redshift bins over the entire simulated light cone for 10 different observers. Full sky coverage up to redshift $z\sim0.15$ and partial sky coverage, i.e. a pencil beam with half opening angle $25^\circ$, for larger redshifts.
• Figure 3: Normalized histograms of the absolute value of the position drift in three different redshift bins $z= 0.1,0.2,0.3\pm0.01$ for ten different observers and best-fit Rayleigh distribution \ref{['eq:rayleigh_dist']} with scale parameter $\sigma$.
• Figure 4: Hexbin density map of the absolute value of the position drift as a function of the redshift. Simulation result (left), prediction according to perturbation theory as given by \ref{['eq:position_drift_pertb_theory']} (centre) and difference between the two (right).
• Figure 5: Normalized histograms of the relative difference between the simulation result and theory prediction according to \ref{['eq:position_drift_pertb_theory']} for the position drift. The top row shows the relative difference in absolute magnitude. The bottom row shows the cosine of the angle between the two vectors. Shown for three different redshift bins $z= 0.1,0.2,0.3\pm0.01$ and ten different observers.