New test of the FLRW metric using the distance sum rule

TL;DR

This paper introduces a new, model-independent test of the FLRW metric's validity by comparing cosmological distances, using supernova and galaxy lensing data, to constrain the universe's spatial curvature.

Contribution

It develops a geometrical optics-based test that does not depend on matter content or Einstein equations, and applies it to observational data to assess the FLRW metric.

Findings

FLRW metric is consistent with current data.

Spatial curvature parameter constrained to -1.22<Ω_K0<0.63.

Systematic uncertainties mainly from lens modeling.

Abstract

We present a new test of the validity of the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric, based on comparing the distance from redshift 0 to $z_1$ and from $z_1$ to $z_2$ to the distance from $0$ to $z_2$. If the universe is described by the FLRW metric, the comparison provides a model-independent measurement of spatial curvature. The test relies on geometrical optics, it is independent of the matter content of the universe and the applicability of the Einstein equation on cosmological scales. We apply the test to observations, using the Union2.1 compilation of supernova distances and Sloan Lens ACS Survey galaxy strong lensing data. The FLRW metric is consistent with the data, and the spatial curvature parameter is constrained to be $-1.22<\Omega_{K0}<0.63$, or $-0.08<\Omega_{K0}<0.97$ with a prior from the cosmic microwave background and the local Hubble constant, though modelling of the lenses is a source of significant systematic uncertainty.