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Modified gravity models require a screening mechanism to be able to evade thestringent constraints from local gravity experiments and, at the same time,give rise to observable astrophysical and cosmological signatures. Suchscreened modified gravity models necessarily have dynamics determined bycomplex nonlinear equations that usually need to be solved on a model-by-modelbasis to produce predictions. This makes testing them a cumbersome process. Inthis paper, we investigate whether there is a common signature for all thedifferent models that is suitable to testing them on cluster scales. To do thiswe propose an observable related to the fifth force, which can beobservationally related to the ratio of dynamical-to-lensing mass of a halo,and then show that the predictions for this observable can be rescaled to anear universal form for a large class of modified gravity models. Wedemonstrate this using the Hu-Sawicki $f(R)$, the Symmetron, the nDGP, and theDilaton models, as well as unifying parametrizations. The universal form isdetermined by only three quantities: a strength, a mass, and a width parameter.We also show how these parameters can be derived from a specific theory. Thisself-similarity in the predictions can hopefully be used to search forsignatures of modified gravity on cluster scales in a model-independent way.

Universal predictions of screened modified gravity on cluster scales