  The $f(R)$ modified gravity theory can explain the accelerating expansion of
the late Universe without introducing dark energy. In this study, we predict
the constraint strength on the $f(R)$ theory using the mock data generated from
the China Space Station Telescope (CSST) Ultra-Deep Field (UDF) Type Ia
supernova (SN Ia) survey and wide-field slitless spectroscopic baryon acoustic
oscillation (BAO) survey. We explore three popular $f(R)$ models, and introduce
a parameter $b$ to characterize the deviation of the f(R) theory from the
$\Lambda$CDM theory. The Markov Chain Monte Carlo (MCMC) method is employed to
constrain the parameters in the $f(R)$ models, and the nuisance parameters and
systematical uncertainties are also considered in the model fitting process.
Besides, we also perform model comparisons between the $f(R)$ models and the
$\Lambda$CDM model. We find that the constraint accuracy using the CSST SN
Ia+BAO dataset alone is comparable to or even better than the result given by
the combination of the current relevant observations, and the CSST SN Ia+BAO
survey can distinguish the $f(R)$ models from the $\Lambda$CDM model. This
indicates that the CSST SN Ia and BAO surveys can effectively constrain and
test the $f(R)$ theory.
