2012ApJ...749..127T

Gravitational lensing can provide pure geometric tests of the structure of spacetime, for instance by determining empirically the angular diameter distance-redshift relation. This geometric test has been demonstrated several times using massive clusters which produce a large lensing signal. In this case, matter at a single redshift dominates the lensing signal, so the analysis is straightforward. It is less clear how weaker signals from multiple sources at different redshifts can be stacked to demonstrate the geometric dependence. We introduce a simple measure of relative shear which for flat cosmologies separates the effect of lens and source positions into multiplicative terms, allowing signals from many different source-lens pairs to be combined. Applying this technique to a sample of groups and low-mass clusters in the COSMOS survey, we detect a clear variation of shear with distance behind the lens. This represents the first detection of the geometric effect using weak lensing by multiple, low-mass groups. The variation of distance with redshift is measured with sufficient precision to constrain the equation of state of the universe under the assumption of flatness, equivalent to a detection of a dark energy component Ω_X at greater than 99% confidence for an equation-of-state parameter -2.5 ≤ w ≤ -0.1. For the case w = -1, we find a value for the cosmological constant density parameter Ω_Λ = 0.85^+0.044_–0.19(68% CL) and detect cosmic acceleration (q₀< 0) at the 98% CL. We consider the systematic uncertainties associated with this technique and discuss the prospects for applying it in forthcoming weak-lensing surveys.