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

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mtext mathvariant="italic">𝑖𝑛 𝑟𝑒𝑎𝑙 𝑡𝑖𝑚𝑒</mml:mtext> </mml:math> . This so-called <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mtext mathvariant="italic">𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑑𝑟𝑖𝑓𝑡</mml:mtext> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mtext mathvariant="monospace">𝚐𝚎𝚟𝚘𝚕𝚞𝚝𝚒𝚘𝚗</mml:mtext> </mml:math> . 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.