A reformulation of general relativity is proposed with the relativity principle being invalid. Consequently the space-time manifold carries a natural (1+3)-foliation, where the foliation variables supersede the metric as the fundamental object. The Einstein equations become modified by some kind of foliation energy, but otherwise remain part of the dynamics. The theory is applied to a homogeneous and isotropic universe; the generation of mass can be explained by conversion of foliation energy and inflation is driven by the negative foliation pressure.