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Dark energy may be the first sign of new fundamental physics in the Universe, taking either a physical form or revealing a correction to Einsteinian gravity. Weak gravitational lensing and galaxy peculiar velocities provide complementary probes of general relativity, and in combination allow us to test modified theories of gravity in a unique way. We perform such an analysis by combining measurements of cosmic shear tomography from the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS) with the growth of structure from the WiggleZ Dark Energy Survey and the Six-degree-Field Galaxy Survey, producing the strongest existing joint constraints on the metric potentials that describe general theories of gravity. For scale-independent modifications to the metric potentials which evolve linearly with the effective dark energy density, we find present-day cosmological deviations in the Newtonian potential and curvature potential from the prediction of general relativity to be ΔΨ/Ψ = 0.05 ± 0.25 and ΔΦ/Φ = −0.05 ± 0.3, respectively (68 per cent confidence limits). [ABSTRACT FROM PUBLISHER]

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 ΩX 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 Ωʌ = 0.85-0.19+0.044 (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. [ABSTRACT FROM AUTHOR]