The XMM Cluster Survey: Testing chameleon gravity using the profiles of clusters

The chameleon gravity model postulates the existence of a scalar field that couples with matter to mediate a fifth force. If it exists, this fifth force would influence the hot X-ray emitting gas filling the potential wells of galaxy clusters. However, it would not influence the clusters' weak lensing signal. Therefore, by comparing X-ray and weak lensing profiles, one can place upper limits on the strength of a fifth force. This technique has been attempted before using a single, nearby cluster (Coma, $z=0.02$). Here we apply the technique to the stacked profiles of 58 clusters at higher redshifts ($0.1<z<1.2$), including 12 new to the literature, using X-ray data from the XMM Cluster Survey (XCS) and weak lensing data from the Canada France Hawaii Telescope Lensing Survey (CFHTLenS). Using a multi-parameter MCMC analysis, we constrain the two chameleon gravity parameters ($\beta$ and $\phi_{\infty}$). Our fits are consistent with general relativity, not requiring a fifth force. In the special case of $f(R)$ gravity (where $\beta = \sqrt{1/6}$), we set an upper limit on the background field amplitude today of $|f_{\rm{R0}}| < 6 \times 10^{-5}$ (95% CL). This is one of the strongest constraints to date on $|f_{\rm{R0}}|$ on cosmological scales. We hope to improve this constraint in future by extending the study to hundreds of clusters using data from the Dark Energy Survey.