# Forecast constraints on $f(T)$ gravity with gravitational waves from compact binary coalescences

## TL;DR

This paper explores how gravitational wave observations from compact binary mergers can be used to constrain $f(T)$ gravity, showing that future detectors like the Einstein Telescope could significantly tighten bounds on the theory's parameters.

## Contribution

It introduces the first analysis of modified gravitational wave propagation in $f(T)$ gravity and forecasts constraints using simulated GW sources for current and future detectors.

## Key findings

- GW amplitude corrections differ from GR in $f(T)$ gravity
- Current GW detectors can match existing cosmological bounds
- Future detectors like ET can improve bounds by up to 2 orders of magnitude

## Abstract

The direct detection of gravitational waves (GWs) opened a new chapter in the modern cosmology to probe possible deviations from the general relativity (GR) theory. In the present work, we investigate for the first time the modified GW form propagation from the inspiraling of compact binary systems within the context of $f(T)$ gravity in order to obtain new forecasts/constraints on the free parameter of the theory. First, we show that the modified waveform differs from the GR waveform essentially due to induced corrections on the GWs amplitude. Then, we discuss the forecasts on the $f(T)$ gravity assuming simulated sources of GWs as black hole binaries, neutron star binaries and black hole - neutron star binary systems, which emit GWs in the frequency band of the Advanced LIGO (aLIGO) interferometer and of the third generation Einstein Telescope (ET). We show that GWs sources detected within the aLIGO sensitivity can return estimates of the same order of magnitude of the current cosmological observations. On the other hand, detection within the ET sensitivity can improve by up to 2 orders of magnitude the current bound on the $f(T)$ gravity. Therefore, the statistical accuracy that can be achieved by future ground based GW observations, mainly with the ET detector (and planed detectors with a similar sensitivity), can allow strong bounds on the free parameter of the theory, and can be decisive to test the theory of gravitation.