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

Yu Song, Yi Zheng

TL;DR

The paper forecasts the CSST survey's ability to test gravity on cosmological scales by measuring the E_G statistic through a harmonic-space framework that jointly uses galaxy–galaxy lensing and clustering. It quantifies how uncertainties, dominated by redshift-space distortions via the parameter $\\beta$, propagate into $E_G$ and explores a μ-Σ parameterization of modified gravity to translate these measurements into constraints on MG parameters $\\mu_0$ and $\\Sigma_0$. Using realistic mock CSST redshift distributions for both photometric and spectroscopic data, the study finds CSST can achieve $E_G$ precision at the few-percent level over $0<z<1.2$ and constrain $\\Sigma_0$ to ~5% (and $\\mu_0$ to ~30–50%), with a dramatic improvement if $\\beta$ is measured to ~1% precision, yielding percent-level $E_G$ and ~1% $\\Sigma_0$ constraints. The results underscore the synergy between weak lensing and spectroscopy and establish a framework for interpreting real CSST data in the context of gravity tests and cosmic acceleration.

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 $β$, 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 $μ-Σ$ modified gravity framework, the parameter $Σ_0$, 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 $β$ to 1\% accuracy, $E_G$ constraints tighten to the percent level, and $Σ_0$ becomes measurable at $\sim 1\%$. 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.

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

TL;DR

The paper forecasts the CSST survey's ability to test gravity on cosmological scales by measuring the E_G statistic through a harmonic-space framework that jointly uses galaxy–galaxy lensing and clustering. It quantifies how uncertainties, dominated by redshift-space distortions via the parameter , propagate into and explores a μ-Σ parameterization of modified gravity to translate these measurements into constraints on MG parameters and . Using realistic mock CSST redshift distributions for both photometric and spectroscopic data, the study finds CSST can achieve precision at the few-percent level over and constrain to ~5% (and to ~30–50%), with a dramatic improvement if is measured to ~1% precision, yielding percent-level and ~1% constraints. The results underscore the synergy between weak lensing and spectroscopy and establish a framework for interpreting real CSST data in the context of gravity tests and cosmic acceleration.

Abstract

We present forecasts for the statistic using redshift distributions of realistic mock galaxy samples from the upcoming Chinese Space Station Survey Telescope (CSST). The dominant uncertainty in stems from the redshift space distortion parameter , whose precision limits the overall constraining power. Our analysis shows that CSST will nevertheless achieve constraints at the few-percent level (3%-9%) over , an improvement by a factor of several to an order of magnitude over current observations. Within the modified gravity framework, the parameter , associated with the effective gravitational constant of the Weyl potential, can be constrained to precision. In a plausible scenario where upcoming spectroscopic surveys determine to 1\% accuracy, constraints tighten to the percent level, and becomes measurable at . 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.
Paper Structure (10 sections, 19 equations, 4 figures, 2 tables)

This paper contains 10 sections, 19 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Analysis framework
  3. Observational definition of EG
  4. Error propagation and covariance estimation
  5. $\mu$--$\Sigma$ parameterization for modified gravity
  6. CSST surveys
  7. Results
  8. $E_G$ predictions
  9. Constraints on modified gravity
  10. Conclusion

Figures (4)

  • Figure 1: Left: Redshift distributions of galaxies in the CSST photometric survey. The distributions are derived from a sub-set of the COSMOS catalog within $1.7\,\mathrm{deg}^2$. We adopt the $\sigma_z = 0.025(1+z)$ sample in our analysis. Right: Galaxy redshift distribution for the CSST slitless spectroscopic (spec-$z$) survey. The distribution is normalized following 2019ApJ...883..203G, and the comoving number density evolution with redshift is also shown.
  • Figure 2: Forecasted $E_G$ measurements in harmonic space. The upper panel shows $E_G(\ell)$ for different combinations of lens and source bins, with error bars denoting Gaussian uncertainties. The lower panel presents the relative statistical uncertainty, $\sigma(E_G)/E_G - 1$, as a function of multipole $\ell$.
  • Figure 3: Left: redshift evolution of the $E_G$ statistic after combining all source bins for each lens bin. Blue points with error bars show the results assuming $\sigma(\beta)/\beta = 1\%$. Percentile numbers beside data points represent the fractional errors of $E_G$. Data represented by hollow red squares show current $E_G$ measurements from the literature collected in table \ref{['tab:eg_literature']}. For clarity and compactness of the figure, the data point at $z=1.5$ in table \ref{['tab:eg_literature']} ($E_G = 0.30 \pm 0.05$Zhang2021) is not shown. Right: Fractional error contributions to the $E_G$ estimator. The bars show the total statistical uncertainty, the error from the measurement of the structure growth rate $\beta$, and the combined contributions from all other sources.
  • Figure 4: $\chi^2$ confidence contours in the $(\mu_0,\Sigma_0)$ plane, derived from the forecasted $E_G$ measurements. The contours represent the $68\%$ and $95\%$ joint confidence regions. Left: Baseline result. $\mu_0 = 0^{+0.483}_{-0.324}, \Sigma_0 = 0^{+0.064}_{-0.052}.$Right: The case where $\sigma(\beta)/\beta$ is set to $1\%$. $\mu_0 = 0^{+0.0908}_{-0.0921}, \Sigma_0 = 0^{+0.0177}_{-0.0184}.$