Abstract We investigate an extension of the standard model of strong and electroweak interactions with classical, nonlinearly realized, conformal invariance. The corresponding Goldstone boson, the dilaton, acquires a small mass due to the conformal anomaly. In curved space, the dilaton is identified with the conformal factor of the metric tensor which also contains the graviton. The corresponding action is invariant only under restricted coordinate transformations which preserve the volume. The theory has no cosmological term and the curvature of the ground state is determined by the vacuum expectation value of the dilaton field, which is an arbitrary integration constant of the gravitational field equations.