Gravitational waves in higher order teleparallel gravity.

The teleparallel equivalent of higher order Lagrangians like L□R = −R + a0R2 + a1R□R can be obtained by means of the boundary term B = 2∇μTμ. In this perspective, we derive the field equations in presence of matter for higher-order teleparallel gravity considering, in particular, sixth-order theories where the □ operator is linearly included. In the weak field approximation, gravitational wave solutions for these theories are derived. Three states of polarization are found: the two standard + and × polarizations, namely 2-helicity massless transverse tensor polarizations, and a 0-helicity massive, with partly transverse and partly longitudinal scalar polarization. Moreover, these gravitational waves (GWs) exhibit four oscillation modes related to four degrees of freedom: the two classical + and × tensor modes of frequency ω1, related to the standard Einstein waves with ; two mixed longitudinal-transverse scalar modes for each frequencies ω2 and ω3, related to two different 4-wave vectors, and. The four degrees of freedom are the amplitudes of each individual mode, i.e. , , , and. To describe a general teleparallel gravity model of order (2p + 2), we used the teleparallel Lagrangian which demonstrates to be not equivalent to. By varying its action, the related field equations in the presence of matter are derived. Hence we obtain the GWs for these teleparallel gravity models, i.e. , that are exactly the Einstein GWs as in f(T) teleparallel gravity. In conclusion, the boundary term B generates extra polarizations and additional modes beyond the standard ones. In particular B2 and B□B terms generate both the additional scalar polarization and the extra scalar modes. [ABSTRACT FROM AUTHOR]