Forecasting the E_G measurements from the photometric and spectroscopic surveys of Chinese Space Station Survey Telescope (CSST)

Abstract

We present forecasts for the $E_G$ statistic using redshift distributions of realistic mock galaxy samples from the upcoming Chinese Space Station Survey Telescope (CSST). The dominant uncertainty in $E_G$ stems from the redshift space distortion parameter $\beta$, whose precision limits the overall constraining power. Our analysis shows that CSST will nevertheless achieve $E_G$ constraints at the few-percent level ($3\%-9\%$) over $0<z<1.2$, an improvement by a factor of several to an order of magnitude over current observations. Within the $\mu -\Sigma$ modified gravity framework, the parameter ${\Sigma }_0$, associated with the effective gravitational constant of the Weyl potential, can be constrained to $\sim 5\%$ precision. In a plausible scenario where upcoming spectroscopic surveys determine $\beta$ to $1\%$ accuracy, $E_G$ constraints tighten to the percent level, and ${\Sigma }_0$ becomes measurable at $\sim 1\%$. For representative modified gravity scenarios, we find that the potential deviations from the Hu--Sawicki $f(R)$ model and the normal-branch Dvali--Gabadadze--Porrati (nDGP) model remain detectable within the expected sensitivity of CSST. These results demonstrate that CSST will serve as a powerful facility for testing gravity and underscore the essential synergy between photometric weak lensing and spectroscopic surveys in probing cosmic acceleration.

15 pages, 6 figures, RAA accepted