Probing gravitational non-minimal coupling with dark energy surveys

We investigate observational constraints on a specific one-parameter extension to the minimal quintessence model, where the quintessence field acquires a quadratic coupling to the scalar curvature through a coupling constant $\xi$. The value of $\xi$ is highly suppressed in typical tracker models if the late-time cosmic acceleration is driven at some field values near the Planck scale. We test $\xi$ in a second class of models in which the field value today becomes a free model parameter. We use the combined data from type-Ia supernovae, cosmic microwave background, baryon acoustic oscillations and matter power spectrum, to weak lensing measurements and find a best-fit value $\xi >0.289$ where $\xi =0$ is excluded outside the 95 per cent confidence region. The effective gravitational constant $G_{\mathrm{e}\mathrm{f}\mathrm{f}}$ subject to the hint of a non-zero $\xi$ is constrained to $-0.003 < 1- G_{\rm eff}/G < 0.033$ at the same confidence level on cosmological scales, and can be narrowed down to $1-G_{\mathrm{e}\mathrm{f}\mathrm{f}}\mathrm{/}G<2.2\times {10}^{-5}$ when combining with Solar System tests.