Distinguish the $f(T)$ model from $\Lambda$CDM model with Gravitational Wave observations

TL;DR

This study demonstrates that combining gravitational wave data with electromagnetic observations can effectively distinguish the $f(T)$ gravity model from the $Lambda$CDM model, especially with future GW measurements like those from the Einstein Telescope.

Contribution

It introduces a method to differentiate $f(T)$ gravity from $Lambda$CDM using simulated GW data combined with EM observations, addressing previous degeneracy issues.

Findings

GW+BAO+CMBR data can distinguish $f(T)$ from $Lambda$CDM at 2$sigma$

Simulated GW data from Einstein Telescope is consistent with current EM data

$H_0$ tension impacts the distinguishability between models

Abstract

Separately, neither electromagnetic (EM) observations nor gravitational wave (GW) observations can distinguish between the $f(T)$ model and the $\Lambda$CDM model effectively. To break this degeneration, we simulate the GW measurement based on the coming observation facilities, explicitly the Einstein Telescope. We make cross-validations between the simulated GW data and factual EM data, including the Pantheon, H(z), BAO and CMBR data, and the results show that they are consistent with each other. Anyway, the EM data itself have the $H_0$ tension problem which plays critical role in the distinguishable problem as we will see. Our results show that the GW$+$BAO$+$CMBR data could distinguish the $f(T)$ theory from the $\Lambda$CDM model in $2\sigma$ regime.