Relation between physical and metric field in general relativity and cosmology

By assuming that the whole matter of the Universe possesses a dilatational degree of freedom, we attempted to show the equivalence between the curvedmetric of space-time and the flat metric of dilated space-time. In the framework of this procedure we supposed that the metrical field and the physical space and time change their roles. The basic result suggests that gravitation and dilatation are interrelated phenomena. In addition we discuss the possibility of the Universe which is of a hybrid type: it possesses at the same time properties of the evolutionary and stationary Universe. Finally, we discuss the lenghtening of day in time as an example which can support our ideas. There was suggested that this phenomenon appears partly as cosmological manifestation.