Gravitational Waves in Modified Teleparallel Theories

TL;DR

This paper analyzes gravitational wave properties in various modified teleparallel theories, revealing differences in polarization modes and perturbation behaviors, which could help distinguish these theories through gravitational-wave observations.

Contribution

It provides the first detailed perturbation analysis of gravitational waves in multiple modified teleparallel theories, highlighting their distinct polarization features and perturbation characteristics.

Findings

$f(T)$ gravity has no extra polarization modes at first-order perturbation.

$f(T,B)$ gravity exhibits additional longitudinal and breathing modes at first-order.

$f(T,T_G)$ gravity's gravitational wave behavior matches that of $f(T)$ gravity.

Abstract

We investigate the gravitational waves and their properties in various modified teleparallel theories, such as $f(T), f(T,B)$ and $f(T,T_G)$ gravities. We perform the perturbation analysis both around a Minkowski background, as well as in the case where a cosmological constant is present, and for clarity we use both the metric and tetrad language. For $f(T)$ gravity we verify the result that no further polarization modes comparing to general relativity are present at first-order perturbation level, and we show that in order to see extra modes one should look at third-order perturbations. For non-trivial $f(T,B)$ gravity, by examining the geodesic deviation equations, we show that extra polarization models, namely the longitudinal and breathing modes, do appear at first-order perturbation level, and the reason for this behavior is the fact that although the first-order perturbation does not have any effect on $T$, it does affect the boundary term $B$. Finally, for $f(T,T_G)$ gravity we show that at first-order perturbations the gravitational waves exhibit the same behavior to those of $f(T)$ gravity. Since different modified teleparallel theories exhibit different gravitational wave properties, the dvancing gravitational-wave astronomy would help to alleviate the degeneracy not only between curvature and torsional modified gravity but also between different subclasses of modified teleparallel gravities.