The New Interpretation of the Uniformly Expanding Universe
  The spacetime structure of the spatially uniformly expanding universe is described in terms of a kind of global space and global time instead of the space and time we usually recognize. The global space at some instant is a space in which the global time is equal and the global time is equal to the proper time of any point moving together with the expansion of the universe which has elapsed since the big bang. The universe descibed in terms of the global space and time thus defined is open spatially and the Einstein's equations give a solution that the space expands eternally regardless of the mass density of the universe indicating that any expanding universe is open dynamically as well, as it is the case only when the density is less than the critical value in the standard model. In fact the critical density has not any particular meaning in the new frame. Finally the equations for the light path in the new frame are studied and are found similar to those in the standard model. 
Yoshio Kubo