On the possible line elements for the universe

Introduction. - As is well known, two different line elements, both compatible with general relativity, have been proposed respectively by Einstein and by de Sitter for the treatment of the large-scale behavior of the universe as a whole. Since neither of these line elements appears to account in any very direct or inevitable way for our present observational facts with regard to the distances and Doppler shifts for the extragalactic nebulae,(1) it is interesting to inquire whether these are the only possible line elements that could be proposed as applicable to cosmological behavior.