Interactive quadratic gravity

A quadratic semiclassical theory, regarding the interaction of gravity with a massive scalar quantum field, is considered in view of the renormalizable energy–momentum tensor in a multi-dimensional curved spacetime. According to it, a self-consistent coupling between the square curvature term R2 and the quantum field Φ(t,x→ ) should be introduced in order to yield the “correct” renormalizable energy–momentum tensor in quadratic gravity theories. The subsequent interaction discards any higher-order derivative terms from the gravitational field equations, but, in the expense, it introduces a geometric source term in the wave equation for the quantum field. Unlike the conformal coupling case (∼RΦ2), this term does not represent an additional “mass” and, therefore, the quantum field interacts with gravity not only through its mass (or energy) content (∼Φ2), but, also, in a more generic way (R2Φ). Within this context, we propose a general method to obtain mode-solutions for the quantum field, by means of the associated Greenʹs function in an anisotropic six-dimensional background.