Testing f(R) gravity with the simulated data of gravitational waves from the Einstein Telescope

TL;DR

This study assesses how gravitational wave data from the Einstein Telescope can constrain and differentiate between modified gravity models, specifically f(R) theories, using simulated data combined with electromagnetic observations.

Contribution

It introduces a method to use simulated third-generation GW data to test and constrain f(R) gravity models, highlighting the potential of GWs as independent probes of cosmology.

Findings

GW data can effectively break parameter degeneracies in f(R) models.

Current data favor the cosmological constant over modified gravity models.

Future GW observations will better test the consistency of ΛCDM with modified gravity.

Abstract

In this paper we analyze the implications of gravitational waves (GWs) as standard sirens on the modified gravity models by using the third-generation gravitational wave detector, i.e., the Einstein Telescope. Two viable models in $f(R)$ theories within the Palatini formalism are considered in our analysis ($f_{1}(\mathcal{R})=\mathcal{R}-\frac{\beta}{\mathcal{R}^{n}}$ and $f_{2}(\mathcal{R})=\mathcal{R}+\alpha\ln{\mathcal{R}}-\beta$), 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 sirens 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 most recent EM observations will reveal the consistency or acknowledge the tension between the $\Lambda$CDM model and modified gravity theories.