  We study and model the properties of galaxy clusters in the normal-branch
Dvali-Gabadadze-Porrati (nDGP) model of gravity, which is representative of a
wide class of theories which exhibit the Vainshtein screening mechanism. Using
the first cosmological simulations which incorporate both full baryonic physics
and nDGP, we find that, despite being efficiently screened within clusters, the
fifth force can raise the temperature of the intra-cluster gas, affecting the
scaling relations between the cluster mass and three observable mass proxies:
the gas temperature, the Compton $Y$-parameter of the Sunyaev-Zel'dovich effect
and the X-ray analogue of the $Y$-parameter. Therefore, unless properly
accounted for, this could lead to biased measurements of the cluster mass in
tests that make use of cluster observations, such as cluster number counts, to
probe gravity. Using a suite of dark-matter-only simulations, which span a wide
range of box sizes and resolutions, and which feature very different strengths
of the fifth force, we also calibrate general fitting formulae which can
reproduce the nDGP halo concentration at percent accuracy for $0\leq z\leq1$,
and halo mass function with $\lesssim3\%$ accuracy at $0\leq z\leq1$
(increasing to $\lesssim5\%$ for $1\leq z\leq 2$), over a halo mass range
spanning four orders of magnitude. Our model for the concentration can be used
for converting between halo mass overdensities and predicting statistics such
as the nonlinear matter power spectrum. The results of this work will form part
of a framework for unbiased constraints of gravity using the data from ongoing
and upcoming cluster surveys.
