### Abstract

An accepted explanation for the accelerated expansion of the late-time Universe is to modify the Einstein equation, either by adding a component to the energy-momentum tensor via dark energy, or to the Einstein tensor via a modification to gravity. The second of these options often involves the introduction of a scalar field, which couples to the matter components of the Universe and gives rise to a fifth force, of the same order of magnitude as gravity. Through a variety of experiments and astronomical observations, this fifth force has been demonstrated to be negligible on Terrestrial and Solar System scales. Therefore if it does act on large scales, it must be suppressed, or `screened', on small scales.In this thesis, I place constraints upon one of these screening methods, chameleon gravity. Chameleon gravity 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 cluster's weak lensing signal. Therefore, by comparing X-ray and weak lensing profiles, upper limits can be placed on the strength of a fifth force.

To do so I first present two hydrodynamical simulations, one evolved under CDM+GR and the other under f(R). From these two simulations I generate X-ray surface brightness and weak lensing profiles for a number of simulated clusters. Using these profiles I test many of the assumptions of the technique used to constraint If

_{R0}I. I then use these profiles to test the analytic pipelines developed to constrain f(R) gravity by applying a full MCMC analysis. From doing so I find constraints on the modified gravity parameters of If

_{R0}I< 8:3 x10

^{-5}.

Next I outline the creation of a sample of 58 clusters, including 12 new to the literature, with high quality weak lensing data from CFHTLenS and X-ray data from XCS. By stacking these clusters I use a multi-parameter MCMC analysis to constrain the two chameleon gravity parameters ( ß and φ

_{∞}). The fits are consistent with general relativity, not requiring a fifth force. In the special case of f(R) gravity (where ß = √1/6), I set an upper limit on the background field amplitude today of If

_{R0}I< 6 x 10-5 (95% CL). This is one of the strongest constraints to date on If

_{R0}I on cosmological scales. These fits are also found to be consistent with those recovered from the f(R) simulations.

Finally I look at the future of this method, beginning with forecasting the constraints that this technique will be able to place on f(R) gravity using the Dark Energy Survey, finding If

_{R0}I> 2 x 10

^{-5}. Next I discuss how the X-ray surface brightness profiles might be improved by removing contaminating point sources from the X-ray images and find that doing so leads to a reduction in the error bars of 5%. I end this thesis by detailing how the techniques discussed within can be applied to constrain other modified gravity theories, namely the Vainshtein mechanism. Doing so I am able to place competitive constraints upon Vainshtein gravity, including the first ever constraint on a particular parametrisation.

Date of Award | Nov 2016 |
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Original language | English |

Supervisor | Bob Nichol (Supervisor) & David Bacon (Supervisor) |