Cosmic curvature tested directly from observations

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 ∼ 6 × 10 −3 level.

Direct test of the FLRW metric from strongly lensed gravitational wave observations

“…Instead, we fit a constant Ω k to the data and consider the accuracy of fit. The problem was previously recognized by 15 and extensively discussed in 17 , with a heuristic suggestion that appropriate weighting on the Ω k estimator can provide a substantially unbiased result. Therefore, in order to clarify and study the systematics and scatter in our results, we will make summary statistics in three ways: standard weighted mean, modified weighted mean, and median statistics.…”

“…Recently 15 , presented a new test of the validity of the FLRW metric, using the combination of independent observations: Union2.1 supernova distances and galaxy strong lensing data from Sloan Lens ACS Survey. Let us note that the previous works focused on the reconstruction of a smooth distance function with supernova data, which were used to estimate the luminosity distance to lenses and sources 16,17 .…”

Low-redshift measurement of the sound horizon through gravitational time-delays

“…Shajib et al 2019). Future measurements of gravitational time delays from the Large Synoptic Survey Telescope can reach percent-level precision (Liao et al 2015), making this method a highly competitive probe (Denissenya et al 2018).…”

Strongly gravitationally lensed type Ia supernovae: Direct test of the Friedman-Lemaître-Robertson-Walker metric

“…One should be very careful to the bias induced by the Ω k measurements with large uncertainties. The most straightforward way of summarizing multiple measurements is inverse variance weighting [66,67]…”