The production of matter from curvature in a particular linearized high order theory of gravity and the longitudinal response function of interferometers

The strict analogy between scalar-tensor theories of gravity and high order gravity is well known in the literature. In this paper it is shown that, from a particular high order gravity theory known in the literature, it is possible to produce, in the linearized approach, particles which can be seen like massive scalar modes of gravitational waves, and the response of interferometers to such particles is analysed. The presence of the mass generates a longitudinal force in addition of the transverse one which is appropriate to the massless gravitational waves and the response of an arm of an interferometer to this longitudinal effect in the frame of a local observer is computed. This longitudinal response function is directly connected to the function of the Ricci scalar in the particular action of this high order theory. Important consequences from a theoretical point of view could arise from this approach, because it opens up the possibility of using the signals seen from interferometers to understand which is the correct theory of gravitation. The presence of the mass could also have important applications in cosmology because of the fact that gravitational waves can have mass and could give a contribution to the dark matter of the Universe.