Redshift drift in a universe with structure III: Numerical relativity

TL;DR

This study computes the cosmic redshift drift within fully relativistic cosmological simulations, using the Einstein Toolkit and a GR ray-tracer to track 50 observers across the sky to $z\approx 1$. It finds that the mean drift tracks the EdS expectation to sub-percent accuracy over cosmological redshifts, while substantial sky-to-sky fluctuations (up to $10$–$30\%$ at low to moderate $z$) exist due to inhomogeneities, with a persistent dipole pattern in the angular distribution. The redshift-drift signal decomposes into Ricci and Weyl contributions that largely cancel on average, though local Weyl dominance can yield positive drifts at very low $z$; this has implications for interpreting upcoming measurements by SKA and ELT in the presence of realistic structure. The results emphasize the importance of sky coverage and angular structure when forecasting and analyzing redshift-drift data from next-generation facilities.

Abstract

Measurements of the cosmic redshift drift - the change in redshift of a source over time - will enable independent detection of cosmological expansion thanks to the immense precision soon reached by new facilities such as the Square Kilometer Array Observatory and the Extremely Large Telescope. We conduct the first ever redshift drift computation in fully relativistic cosmological simulations, with the simulations performed with the Einstein Toolkit. We compute the redshift drift over the full skies of 50 synthetic observers in the simulation. We compare all-sky averages for each observer - and across all observers - to the Einstein-de Sitter (EdS) model which represents the large-scale spatially-averaged spacetime of the simulation. We find that at $z\approx0.2$ the mean redshift drift across the sky for all observers deviates from the EdS prediction at the percent level, reducing to $\sim0.1\%$ by $z\approx 1$. However, fluctuations in the redshift drift across the sky are $\sim 10-30\%$ at $z\approx 0.1$ and a few percent at $z\approx 0.5$. Such fluctuations are large enough to potentially exceed the expected precision of upcoming redshift drift measurements. Additionally, we find that along 0.48% of the light rays the redshift drift becomes temporarily positive at very low redshift of $z\lesssim 0.02$. This occurs despite our simulation data being based on a matter-dominated model universe. By including a cosmological constant, we expect a slower growth of structures than in the leading-order EdS space-time, and this may reduce the anisotropy over the observers' skies, although we generally expect our results to hold as order-of-magnitude estimates. Redshift drift is arguably one of the most important measurements to be made by next-generation telescopes. Our results collectively serve as preparation for interpreting such a measurement in the presence of realistic cosmic structures.

Figures (12)

• Figure 1: Mean and fluctuations of the redshift drift along 768 random light rays each for 50 randomly placed present-time observers. The redshift drift is shown relative to the EdS redshift drift. The dark and light shaded regions show the 68.1% and 95.4% percentiles across all light rays, respectively.
• Figure 2: Mean and fluctuations of the Weyl and Ricci contributions to the redshift drift for 50 observers with 768 lines of sight each. The dark and light shaded area shows the 68.1% and 95.4% percentiles across all light rays for the Ricci component, respectively, while the same is shown for the Weyl component with dashed curves.
• Figure 3: The curve shows the mean of the redshift drift along 768 light rays for 50 observers. The grey shaded region shows the maximum to minimum fluctuations of $\delta z$ across all light rays.
• Figure 4: Mean redshift drift across 768 lines of sight for 50 observers as a function of redshift, $z$. We show the absolute value of $\delta z$ normalised by the background EdS prediction, $\delta z_{\rm EdS}$.
• Figure 5: All-sky maps of the redshift drift, $\delta z$, relative to the background EdS value for three sample observers at two redshift slices $z\approx 0.1$ and $z\approx 0.5$. Each observer has $N_{\rm side}=32$ lines of sight in directions of HEALPix indices.