Constraining Brans-Dicke cosmology with the CSST galaxy clustering
  spectroscopic survey
  The Brans-Dicke (BD) theory is the simplest Scalar-Tensor theory of gravity,
which can be considered as a candidate of modified Einstein's theory of general
relativity. In this work, we forecast the constraints on BD theory in the CSST
galaxy clustering spectroscopic survey with a magnitude limit $\sim 23$ AB mag
for point-source 5$\sigma$ detection. We generate mock data based on the
zCOSMOS catalog and consider the observational and instrumental effects of the
CSST spectroscopic survey. We predicate galaxy power spectra in the BD theory
from $z=0$ to 1.5, and the galaxy bias and other systematical parameters are
also included. The Markov Chain Monte Carlo (MCMC) technique is employed to
find the best-fits and probability distributions of the cosmological and
systematical parameters. A Brans-Dicke parameter $\zeta$ is introduced, which
satisfies $\zeta=\ln \left(1+\frac{1}{\omega}\right)$. We find that the CSST
spectroscopic galaxy clustering survey can give $|\zeta|<10^{-2}$, or
equivalently $|\omega|>\mathcal{O}(10^2)$ and $|\dot{G}/G|<10^{-13}$, under the
assumption $\zeta = 0$. These constraints are almost at the same order of
magnitude compared to the joint constraints using the current cosmic microwave
background (CMB), baryon acoustic oscillations (BAO), and Type Ia supernova (SN
Ia) data, indicating that the CSST galaxy clustering spectroscopic survey would
be powerful to constrain the BD theory and other modified gravity theories.
