Bending of light in the framework of R + R2 gravity

Abstract

We present a tree level approach to the issue of the de ection of photons by the gravitational eld of the Sun, treated as an external eld, on the basis of R + R 2 gravity. We show that the de ection angle of a photon grazing the surface of the Sun is exactly the same as that given by general relativity. An explanation for this strange coincidence is provided.

Propagator, tree-level unitarity and effective nonrelativistic potential for higher-derivative gravity theories in D dimensions

“…So, the potential for linearized higher-derivative gravity is given by the expression 4,7 V͑r ͒ϭGm ͫ Ϫ From the computation of V(r) for linearized quadratic gravity in three and four dimensions we learned that the existence of the potential is related to the absence of tachyons in the dynamical field. Consequently, we may conjecture that this is so in any dimension DϾ2.…”

“…In a series of papers on the photon propagation around a massive body in quadratic theories of gravitation it was shown that, unlike Einstein's gravity, quadratic gravity produces dispersive photon propagation. [7][8][9] To be more specific, quadratic gravity produces energy-dependent photon scattering. An interesting consequence of this fact is that gravity's rainbows and higher-derivative gravity can coexist without conflict.…”

“…In addition, it was also found that the gravitational deflection predicted by quadratic gravity is always smaller than that predicted by Einstein's theory. [7][8][9] It is worth mentioning that the R 2 sector of the theory of gravitation with higher derivatives does not contribute anything to the gravitational deflection. 10,11 After this little digression we return to the question raised previously.…”

“…[7][8][9] It is worth mentioning that the R 2 sector of the theory of gravitation with higher derivatives does not contribute anything to the gravitational deflection. 10,11 After this little digression we return to the question raised previously. Our motivation for studying D-dimensional higher-derivative gravity theories is to try to answer, among other things, the following questions:…”

On the gravitational seesaw in higher-derivative gravity

“…On the other hand, the R + R 2 model is equivalent to the Brans-Dicke theory with a massive degree of freedom. It is possible to show that the light bending alone cannot distinguish between this type of metric-scalar gravity theories and general relativity [32][33][34][35]. In these references one can find the discussion concerning the difference with the massless Brans-Dicke theory [36], in which the mass of the massive body (e.g., a star or galaxy) creating the gravitational field must be renormalized.…”