Will the universe expand forever?
In principle, observation should allow determination of which model corresponds to the real universe. One observational test is based upon deducing the geometry of the universe, say by number counts of some type of astronomical object whose properties have not changed over time. As a function of distance, in a flat universe, the number of objects should increase in proportion to the volume of space sample, or as N(r) ∝ r3, with each increase of a factor of 2 in distance producing an increase in the number of objects by 23 = 8 times. In a positively curved universe, the number increases at a lesser rate, but in a negatively curved universe, the number increases more rapidly. Alternatively, because the strength of gravity slowing the expansion of the universe is a direct consequence of the mass density, determination of the rate of deceleration constitutes a second potential test. Greater mass means more deceleration, thus a past expansion is much more rapid than at present. This should
