Perturbative Quantum Gravity in Analogy with Fermi Theory of Weak Interactions using Bosonic Tensor Fields

In this paper we work in perturbative quantum gravity and we introduce a new effective model for gravity. Expanding the Einstein-Hilbert Lagrangian in graviton field powers we have an infinite number of terms. In this paper we study the possibility of an interpretation of more than three graviton interacting vertices as effective vertices of a most fundamental theory that contain tensor fields. Here we introduce a Lagrangian model named I.T.B (Intermediate Tensor Boson) where four gravitational "pseudo-currents" that contain two gravitons couple to three massive tensorial fields of rank 1, 3, 5 respectively. We show that the exchange of those massive particles reproduces, at low energy, the interacting vertices for four or more gravitons. In a particular version, the model contains a dimensionless coupling constant "g" and the mass M of the intermediate bosons as free parameters. The universal gravitational constant G is shown to be proportional to the inverse of mass squared of mediator fields. A foresighting choice of the dimensionless coupling constant could lower the energy scale where quantum gravity aspects show up.