Modeling halo mass functions in chameleon<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity

On cosmological scales, observations of the cluster abundance currently place the strongest constraints on $f(R)$ gravity. These constraints lie in the large-field limit, where the modifications of general relativity can correctly be modeled by setting the Compton wavelength of the scalar field to its background value. These bounds are, however, at the verge of penetrating into a regime where the modifications become nonlinearly suppressed due to the chameleon mechanism and cannot be described by this linearized approximation. For future constraints based on observations subjected to cluster abundance, it is therefore essential to consistently model the chameleon effect. We analyze descriptions of the halo mass function in chameleon $f(R)$ gravity using a mass- and environment-dependent spherical collapse model in combination with excursion set theory and phenomenological fits to $N$-body simulations in the $\ensuremath{\Lambda}\mathrm{CDM}$ and $f(R)$ gravity scenarios. Our halo mass functions consistently incorporate the chameleon suppression and cosmological parameter dependencies, improving upon previous formalisms and providing an important extension to $N$-body simulations for the application in consistent tests of gravity with observables sensitive to the abundance of clusters.

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