Cosmic Curvature Tested Directly from Observations

TL;DR

This paper introduces a model-independent geometric method to measure the Universe's spatial curvature directly from observations, using strong lensing and supernova data, enabling precise curvature estimation without assuming specific energy models.

Contribution

It develops two curvature estimators that crosscheck each other and map curvature across redshifts, advancing direct geometric measurement techniques.

Findings

Curvature can be measured at ~6×10^{-3} precision with next-generation data.

The methods do not rely on assumptions about the Universe's energy components.

Estimators can test the constancy of curvature across redshift slices.

Abstract

Cosmic spatial curvature is a fundamental geometric quantity of the Universe. We investigate a model independent, geometric approach to measure spatial curvature directly from observations, without any derivatives of data. This employs strong lensing time delays and supernova distance measurements to measure the curvature itself, rather than just testing consistency with flatness. We define two curvature estimators, with differing error propagation characteristics, that can crosscheck each other, and also show how they can be used to map the curvature in redshift slices, to test constancy of curvature as required by the Robertson-Walker metric. Simulating realizations of redshift distributions and distance measurements of lenses and sources, we estimate uncertainties on the curvature enabled by next generation measurements. The results indicate that the model independent methods, using only geometry without assuming forms for the energy density constituents, can determine the curvature at the $\sim6\times10^{-3}$ level.