Testing Emergent Gravity on Galaxy Cluster Scales

Abstract: Verlinde's theory of Emergent Gravity (EG) describes gravity as an emergent phenomenon rather than a fundamental force. Applying this reasoning in de Sitter space leads to gravity behaving differently on galaxy and galaxy cluster scales; this excess gravity might offer an alternative to dark matter. Here we test these ideas using the data from the Coma cluster and from 58 stacked galaxy clusters. The X-ray surface brightness measurements of the clusters at $0.1 < z < 1.2$ along with the weak lensing data are used to test the theory. We find that the simultaneous EG fits of the X-ray and weak lensing datasets are significantly worse than those provided by General Relativity (with cold dark matter). For the Coma cluster, the predictions from Emergent Gravity and General Relativity agree in the range of 250 - 700 kpc, while at around 1 Mpc scales, EG total mass predictions are larger by a factor of 2. For the cluster stack the predictions are only in good agreement at around the 1 - 2 Mpc scales, while for $r \gtrsim 10$ Mpc EG is in strong tension with the data. According to the Bayesian information criterion analysis, GR is preferred in all tested datasets; however, we also discuss possible modifications of EG that greatly relax the tension with the data.