Gravitational waves in modified teleparallel theories

Abstract

We investigate the gravitational waves and their properties in various modified teleparallel theories, such as f (T ), f (T, B) and f (T, TG) 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, TG) 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 advancing 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.

Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T,B) Gravity with Observational Constraints

“…Ultimately, this implies that the torsion scalar is of at least second order. Observe that this result holds true even if the Weitzenböck gauge is not imposed [69].…”

“…This fact alone guarantees that f (T ) gravity will not exhibit Gauss-Ostrogradsky ghosts since it remains second-order. f (T ) gravity also shares other properties with TEGR such as its GW polarization signature [69,70].…”

“…This is achieved by a coordinate transformation, as prescribed in Eq. (69). This eventually produces Eq.…”

“…In this work, we investigate the gravitomagnetic effects of f (T, B) gravity and its effect on observational constraints of the theory for particular models of this setting [69,[71][72][73][74][75][76]. To do this, we need the field equations of the theory, which are determined by a variation of the f (T, B) gravitational Lagrangian density, ef (T, B) to give [13,14,77]…”

“…where subscripts denote derivatives, and Θ ν ρ is the regular energy-momentum tensor. The spin connection is taken to be zero [69,[71][72][73] since this will be a demand in the work that follows. We will revisit this statement at various stages of the analysis to confirm the consistency of the work.…”