This paper shows how combining measurements from gravitational waves and ordinary light can test a core assumption of cosmology, the Friedmann model, without assuming a particular model for dark energy. The Friedmann model is the mathematical framework used to describe an expanding, homogeneous universe. The authors derive equations that relate two kinds of distance measurements — the gravitational-wave luminosity distance and the electromagnetic (light) luminosity distance — and use those relations to check whether the Friedmann picture holds and to probe the curvature of space.

What the researchers did was purely theoretical. Starting from the usual equations for how waves propagate in an expanding universe, and assuming general relativity and a massless graviton, they derive formulas that express the spatial curvature parameter in terms of the two measured distances. They also show how to get the expansion rate H(z) from gravitational-wave observations, and from those ingredients they build a general “consistency relation” that must hold in any Friedmann universe. As a special case, they give a separate multimessenger test that would indicate whether dark energy behaves exactly like a cosmological constant (the simplest dark energy model).

Why this matters: gravitational waves provide a new, independent way to measure distances in the universe. By comparing those distances with the traditional electromagnetic distances (for example, from supernovae or other bright sources), one can test key aspects of cosmology without having to assume a specific form for dark energy or the values of density parameters. One practical outcome the authors highlight is an expression that estimates the curvature of the universe directly from the difference between the two kinds of distance. Another result is a formula that, if violated by observations, would show that dark energy is not the cosmological constant.