Non-Euclideanism in general relativity and cosmology

Consideration is given to the possibility that the whole matter of the Universe possesses a dilatational degree of freedom. This effect is assumed to be a cause requiring the use of non-Euclidean geometry in the framework of general relativity and cosmology. In this case, however, we assert that non-Euclideanism does not reflect an intrinsic property of the space. Accordingly we propose the concept of a finite and unbounded universe whose extent has nothing to do with the shape of the hypersphere.