General relativity as the low-energy limit in higher derivative quantum gravity

The curvature induced phase transition in quantum R2-gravity with matter is investigated. The renormalization group approach is used to calculate the effective potential with accuracy to linear curvature terms. The universal expressions for induced gravitational and cosmological constants are obtained. The effective potential, induced cosmological and gravitational constants depend on the coupling constants of the original theory and on the gauge parameters. When matter is described by a scalar field, coupling constants subject to asymptotic freedom are chosen. Then a curvature induced phase transition is possible. If the Vilkovisky-De Witt effective action formalism is used then the induced gravitational and cosmological constants do not depend on gauge parameters.