Testing F(R) Gravity With The Simulated Data Of Gravitational Waves From The Einstein Telescope

In this paper we analyze the implications of gravitational waves (GWs) as standard sirens on the modified gravity models by using the third-generation GW detector, i.e., the Einstein Telescope. Two viable models in f(R) theories within the Palatini formalism are considered in our analysis (f(1) (R) = R - beta/R-n and f(2) (R) = R + alpha ln R - beta), with the combination of simulated GW data and the latest electromagnetic (EM) observational data (including the recently released Pantheon type Ia supernovae sample, the cosmic chronometer data, and baryon acoustic oscillation distance measurements). Our analysis reveals that the standard siren GWs, which provide an independent and complementary alternative to current experiments, could effectively eliminate the degeneracies among parameters in the two modified gravity models. In addition, we thoroughly investigate the nature of geometrical dark energy in the modified gravity theories with the assistance of Om(z) and statefinder diagnostic analysis. The present analysis makes it clear-cut that the simplest cosmological constant model is still the most preferred by the current data. However, the combination of future naturally improved GW data and the most recent EM observations will reveal the consistency or acknowledge the tension between the Lambda CDM model and modified gravity theories.