Semiclassical Quadratic Gravity Revisited

The semiclassical interaction of the gravitational with a quantum scalar field is considered, in view of the renormalizability of the associated energy-momentum tensor in a n-dimensional curved spacetime resulting from a quadratic gravitational lagrangian. It is shown that, in this case, a novel coupling between the square curvature term, ${\mathcal{R}}^2$, and the quantum field needs to be introduced. The interaction so considered, discards any higher-order derivative terms from the associated gravitational field equations, but, at the expense, it introduces a geometric source term in the wave equation for the quantum field. Unlike the conformal coupling case, this term does not represent an additional mass; hence, in quadratic gravity theories, quantum fields can interact with gravity in a more generic way and not only through their mass (or energy) content.