Interactive quadratic gravity

Abstract

A quadratic semiclassical theory, regarding the interaction of gravity with a massive scalar quantum field, is considered in view of the renormalizable energymomentum tensor in a multi-dimensional curved spacetime. According to it, a self-consistent coupling between the square curvature term R 2 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 expence, it introduces a geometric source term in the wave equation for the quantum field. Unlike the conformal coupling case (∼ RΦ 2 ), this term does not represent an additional "mass" and, therefore, the quantum field interacts with gravity not only through its mass (or energy) content (∼ Φ 2 ), but, also, in a more generic way (R 2 Φ). Within this context, we propose a general method to obtain mode-solutions for the quantum field, by means of the associated Green's function in an anisotropic six-dimensional background.

Quadratic quantum cosmology with Schutz' perfect fluid

“…To simplify this Lagrangian, we define the variable φ as f ′ (R) = φ, in terms of which the Lagrangian (7) reads…”

“…In this context, renormalization of the energy-momentum tensor for a quantum field in a four-dimensional, curved space-time indicates that the presence of quadratic terms in the gravitational action is a priori expected [6]. On the other hand, Kleidis et al [7], demonstrated that, in quadratic gravity theories, an additional coupling arises between R 2 and any massive quantum scalar field, introducing a geometric source term in the wave equation for the quantum field.…”

Kaluza–Klein higher-derivative induced gravity

“…with a purely geometric source. Although the equation L = 0 is not exactly a Klein-Gordon equation of the form (∂ 2 + m 2 + R/5)φ = αR 2 studied in [19], both theories appear to have a similar physical origin. It was shown that an effective re-normalized Lagrangian of the form αφR 2 is a result of dimensional consideration.…”

“…It was shown that an effective re-normalized Lagrangian of the form αφR 2 is a result of dimensional consideration. Indeed, the coupling constant α can only be made dimensionless, rendering a system free from introducing any additional arbitrary length scale, if the space-time dimension N = 6 [19]. Note that the scalar fields ψ and φ, both with dimension one, considered in this paper are designed to replace all dimensionful coupling constants with appropriate scalar fields.…”

“…It was shown that an effective re-normalized Lagrangian of the form αφR 2 is a result of dimensional consideration. Indeed, the coupling constant α can only be made dimensionless, rendering a system free from introducing any additional arbitrary length scale, if the space-time dimension N = 6 [19].…”