Halo modelling in chameleon theories

We analyse modelling techniques for the large-scale structure formed in scalartensor theories of constant Brans-Dicke parameter which match the concordance model background expansion history and produce a chameleon suppression of the gravitational modi fi cation in high-density regions. Thereby, we use a mass and environment dependent chameleon spherical collapse model, the Sheth-Tormen halo mass function and linear halo bias, the Navarro-Frenk-White halo density pro fi le, and the halo model. Furthermore, using the spherical collapse model, we extrapolate a chameleon mass-concentration scaling relation from a Lambda CDM prescription calibrated to N-body simulations. We also provide constraints on the model parameters to ensure viability on local scales. We test our description of the halo mass function and nonlinear matter power spectrum against the respective observables extracted from large-volume and high-resolution N-body simulations in the limiting case of f (R) gravity, corresponding to a vanishing Brans-Dicke parameter. We fi nd good agreement between the two; the halo model provides a good qualitative description of the shape of the relative enhancement of the f (R) matter power spectrum with respect to Lambda CDM caused by the extra attractive gravitational force but fails to recover the correct amplitude. Introducing an e ff ective linear power spectrum in the computation of the two-halo term to account for an underestimation of the chameleon suppression at intermediate scales in our approach, we accurately reproduce the measurements from the N-body simulations.