A model for cosmology that is conformal invariant from the beginning is presented. Breakdown of the conformal symmetry produces gravitation with parameters of mass. The system initially contains the Hilbert Lagrangian for general relativity plus quadratic terms in the Ricci tensor and in the scalar curvature. All these terms are supposed to create a space–time which cannot exist without gravity. So, masses appear when conformal invariance is broken. Massless Yang–Mills fields appear also as fundamental fields in the Lagrangian. An exact classical solution exists if a conformal scalar boson is introduced also in a conformal manner that couples gravity to the Yang–Mills sector. The paper claims that before the breakdown the model is renormalisable due to its conformal invariant nature.