Einstein-Hilbert gravity, higher derivatives and a scalar matter field

The present paper extends two previous one’s on pure gravity dealing with Einstein-Hilbert and higher derivatives by including a massless scalar field as representative of matter. We study the renormalization to all orders of perturbation theory, provide the Slavnov-Taylor identity, symmetric partial differential equations and derive finiteness properties in the Landau gauge. It is shown that beginning with one-loop negative norm states originating from higher derivatives disappear.