Size and relevance of cosmic backreaction in the real universe

Determine the size and relevance of cosmic backreaction in the real universe.

Background

The paper explains that existing relativistic cosmological simulation frameworks either suppress backreaction through periodic boundary conditions or are insufficiently nonlinear to quantify it realistically. For gevolution, elliptic constraint equations couple all spatial points on a hypersurface, preventing a causally isolated central-region test of boundary effects. Simulations based on the Einstein Toolkit avoid this specific issue but remain only mildly nonlinear, whereas significant backreaction is expected to be a nonlinear relativistic effect.

Because of these limitations, the paper states that the realism of current simulations with respect to backreaction, and consequently the reliability of their indication that global backreaction is small, is unresolved. The authors therefore identify the actual magnitude and importance of cosmic backreaction in the real universe as an open question and use simplified silent-universe simulations instead for their proof-of-principle machine-learning study.

References

In fact, different types of astrophysical structures exist at different length scales and whether their gravitational interactions affect the large-scale expansion of the universe is still a debated question.

— Limits on the Inferred Hubble Constant Bias from a Local McVittie Gravitational Field  (2609.16961 - Gregoris, 15 Sep 2026) in Section 1, Introduction

Overall, it is currently unclear to what extent we can consider these simulations realistic in terms of backreaction, and hence also to what extent we can trust their apparent results indicating that backreaction is small on global scales. We will therefore here take the agnostic point of view and consider the size and relevance of backreaction in the real universe an open question.

— Learning the averaged history of an inhomogeneous universe from its present day density field  (2608.27962 - Bendtsen et al., 28 Aug 2026) in Section 2, “Training data”