We present forecasts for constraints on the Hu and Sawicki
f(R) modified gravity model using realistic mock data representative of future cluster and weak lensing surveys. We create mock thermal Sunyaev-Zel’dovich effect selected cluster samples for SPT-3G and CMB-S4 and the corresponding weak gravitational lensing data from next-generation weak-lensing (ngWL) surveys like Euclid and Rubin. We employ a state-of-the-art Bayesian likelihood approach that includes all observational effects and systematic uncertainties to obtain constraints on the
f(R) gravity parameter
log10|fR0|. In this analysis we vary the cosmological parameters
[Ωm,Ωνh2,h,As,ns,log10|fR0|], which allows us to account for possible degeneracies between cosmological parameters and
f(R) modified gravity. The analysis accounts for
f(R) gravity via its effect on the halo mass function which is enhanced on cluster mass scales compared to the expectations within general relativity (GR). Assuming a fiducial GR model, the upcoming cluster dataset
SPT−3G×ngWL is expected to obtain an upper limit of
log10|fR0|<−5.95 at 95% credibility, which significantly improves upon the current best bounds. The
CMB−S4×ngWL dataset is expected to improve this even further to
log10|fR0|<−6.23. Furthermore,
f(R) gravity models with
log10|fR0|≥−6, which have larger numbers of clusters, would be distinguishable from GR with both datasets. We also report degeneracies between
log10|fR0| and
Ωm as well as
σ8 for
log10|fR0|>−6 and
log10|fR0|>−5 respectively. Our forecasts indicate that future cluster abundance studies of
f(R) gravity will enable substantially improved constraints that are competitive with other cosmological probes. Published by the American Physical Society 2024