Safely simplifying redshift drift computations in inhomogeneous cosmologies: Insights from LTB Swiss-cheese models

TL;DR

The paper tackles the challenge of directly measuring redshift drift in an inhomogeneous cosmos and the computational burden of solving 24 coupled ODEs. By analyzing an LTB Swiss-cheese model, it shows that the redshift-drift signal is effectively captured by the two dominant Ricci and Weyl contributions, allowing a reduction to the standard null geodesic equations and achieving percent-level accuracy up to $z\lesssim1$. The results demonstrate near-cancellation between Ricci and Weyl terms, with subdominant shear and position-drift contributions remaining at the subpercent level and not biasing upcoming observations such as SKA or ELT. This provides a practical, robust framework for efficient redshift-drift calculations applicable to more realistic inhomogeneous cosmologies, including potential extension to N-body simulations.

Abstract

One of the most important discoveries in cosmology is the accelerated expansion of the Universe. Yet, the accelerated expansion has only ever been measured {\em in}directly. Redshift drift offers a direct observational probe of the Universe's expansion history, with its sign revealing whether there has been acceleration or deceleration between source and observer. Its detection will mark a major milestone in cosmology, offering the first direct measurement of an evolving expansion rate. Given its epistemic importance, it is essential to understand how its measurements can be biased. One possibility of bias comes from cosmological structures. However, theoretical estimates of such effects are difficult to obtain because computing redshift drift in general inhomogeneous cosmologies is computationally demanding, requiring the solution of 24 coupled ordinary differential equations. In this work, we use Lemaitre-Tolman-Bondi Swiss-cheese models to show that only the two dominant contributions are needed to achieve percent-level accuracy up to $z = 1$. This allows the reduction of the full system of 24 ODEs to the standard null geodesic equations, significantly simplifying the calculation. \newline\indent Although our analysis is based on idealized Swiss-cheese models with spherical structures, we expect that similar simplifications apply to more complex scenarios, including cosmological N-body simulations. Our analysis thus underpins a practical and robust framework for efficient redshift drift computations applicable to a wider range of inhomogeneous cosmologies.

Figures (6)

• Figure 1: Present-time density profile of the considered LTB model. The horizontal axis shows $R$, which to a good approximation corresponds to the proper radial distance.
• Figure 2: Individual terms in the integral expression for the redshift drift (equation \ref{['eq:integral_dz']}) for fiducial light rays with observer placed in the cheese and hole. The bottom panels show the total redshift drift relative to the EdS redshift drift, together with the density fluctuations along the light rays.
• Figure 3: Mean and standard deviation of the redshift drift along 100 light rays with the observers placed in the cheese and the LTB structures, respectively.
• Figure 4: Mean and standard deviation of the individual contributions to the redshift drift (equation \ref{['eq:integral_dz']}) along 100 light rays with the observers placed in the FLRW cheese.
• Figure 5: Mean and standard deviation of the individual contributions to the redshift drift (equation \ref{['eq:integral_dz']}) along 100 light rays with the observers placed in the LTB structures.