$f(T)$ gravity after GW170817 and GRB170817A

TL;DR

This paper investigates $f(T)$ gravity in light of GW170817 and GRB170817A, showing it predicts gravitational waves travel at light speed and identifying a small deviation from General Relativity that could be tested with future observations.

Contribution

It demonstrates that $f(T)$ gravity satisfies gravitational wave speed constraints and introduces a new parameter affecting gravitational wave dispersion, which can be tested in future experiments.

Findings

GW speed in $f(T)$ gravity equals light speed, satisfying observational constraints.

A small deviation from GR in gravitational wave dispersion is identified.

Future gravitational wave measurements could detect this deviation.

Abstract

The combined observation of GW170817 and its electromagnetic counterpart GRB170817A reveals that gravitational waves propagate at the speed of light in high precision. We apply the effective field theory approach to investigate the experimental consequences for the theory of $f(T)$ gravity. We find that the speed of gravitational waves within $f(T)$ gravity is exactly equal to the light speed, and hence the constraints from GW170817 and GRB170817A are trivially satisfied. The results are verified through the standard analysis of cosmological perturbations. Nevertheless, by examining the dispersion relation and the frequency of cosmological gravitational waves, we observe a deviation from the results of General Relativity, quantified by a new parameter. Although its value is relatively small in viable $f(T)$ models, its possible future measurement in advancing gravitational-wave astronomy would be the smoking gun of testing this type of modified gravity.