Considerations on gravitational waves in higher-order local and non-local gravity

Photon frequency shift in curvature-based Extended Theories of Gravity

“…Here some examples of characteristic values 6 for the relation (26), in the case of satellite on the orbit with r B = 3 2 r A : 1.7 × 10 −3 Earth, Therefore, the best constraint is obtained by considering the Moon as gravitational source on which the observer A is sitting. The angular velocity ω A corresponds with the Moon's angular velocity, ω A = 2.70 × 10 −6 rad/s , while the satellite, observer B, is in circular orbit around the Moon at distance r B = 3 2 r A 2.61 × 10 6 m. For this reason, the Moon is the best candidate to test ETG.…”

“…In particular, some models of ETG have been studied in the Newtonian limit [18,19], as well as in the Minkowskian limit [20][21][22][23][24][25][26]. The weak-field limit has to be tested against realistic self-gravitating systems.…”

Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory

“…In theory, several methods have been developed to analyze the polarization of GWs [65][66][67][78][79][80][81][82][83][84], such as the Newman-Penrose (NP) method [65,66], the geodesic deviation (GD) method [67,78], etc. In the following, we investigate the polarization modes of GWs in the Palatini-GBD theory by using these two methods.…”

“…Following the method shown in Refs. [83,84,[86][87][88][89][90][91][92], the amplitudes of six polarizations in the Palatini-GBD theory can be calculated as follows…”

“…Comparing our results with other theoretical results in Refs. [68,[81][82][83][84], it is observed that the polarization modes of GWs in the Palatini-GBD theory are different from the results given in some other gravitational theories. For example, in the massive BD theory [68], it has two standard tensorial modes of GR and two scalar modes (the longitudinal and the breathing modes); In the massless BD theory it owns two standard tensorial modes and one breathing scalar mode [68]; In the f (R) theories, there are two tensorial modes and a massive scalar mode that is a mix of the longitudinal and the transverse breathing polarization [81,82]; In the f (T, B) theory of teleparallel gravity (it is equivalent to f (R) gravity by linearized the field equations in the weak field limit approximation), there are three polarizations [83]: the two standard of general relativity and an additional massive scalar mode, where the boundary term B excites the extra scalar polarization; In the higher order local and non-local theories of gravity, they have three state of polarization and n + 3 oscillation modes [84] (concretely, they are the two transverse tensor (+) and (×) standard polarization modes of frequency ω 1 , and the n + 1 further scalar modes of frequency ω 2 , ..., ω n+2 , each of which has the same mixed polarization, partly longitudinal and partly transverse).…”