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Brane-induced gravity in warped backgrounds and the absence of the radion

“…One can see, that it is analogous to the one obtained in [9]. There exists a theorem about such combinations of products of Bessel and Neumann functions, which asserts that for e kR > 1 this combination is an even function of m/k and its zeros are real and simple [13].…”

“…According to [5,14] there are no gravitational tachyons and ghosts in this case (but the radion field exists because of the absence of the symmetry (15), (16)). But the answer to the question about the radion as a ghost can be obtained only after the exact solving the equations of motion for the linearized gravity (as it was made, for example, in [9] for the RS1 model). Nevertheless, if we retain strong gravity in the bulk (small M * , otherwise all the constructions make no sense) and Ω ind >> e 2kR , the term (27) on brane 1 makes the radion to be a ghost (all the reasonings are the same as in paper [2] for the T ev brane in the Randall-Sundrum model)!…”

Gravity in the stabilized brane world model in the five-dimensional Brans-Dicke theory

“…We consider the case when the matter is located on the brane at y = L, like in the Randall-Sundrum model. To this end we take C = kL, which makes the fourdimensional coordinates on this brane Galilean (see [2,3,4]). …”

“…Note that these equations can also be obtained by linearizing the Einstein equations and the equation for the scalar field, which follow from action (2), in the background defined by solution of form (3), (4).…”

“…This leads to the existence of the massless scalar field -the radion -in the fourdimensional effective theory on the branes. The coupling constant of this field to matter on the negative tension brane, which is assumed to trap the Standard Model fields, appears to be very large, which contradicts experimental data even at the level of classical experiments [2,4]. This problem was solved by introducing an extra scalar field living in the bulk.…”