Forecasting Constraint on the $f(R)$ Theory with the CSST SN Ia and BAO Surveys

TL;DR

This paper assesses how well future CSST SN Ia and BAO surveys can constrain and differentiate $f(R)$ modified gravity models from the standard $\

Contribution

It demonstrates the potential of CSST surveys to effectively constrain $f(R)$ gravity models and distinguish them from $\

Findings

CSST SN Ia+BAO data can outperform current observations in constraining $f(R)$ models.

The surveys can effectively differentiate $f(R)$ models from $\

CSST data alone provides constraints comparable to combined current observations.

Abstract

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.