Does μ<1 imply that the universe will expand forever?

Abstract

The issue of whether the present observational evidence that the mean mass density of the universe is less than the critical density (i.e., μ<1) implies an infinite future expansion of the universe is discussed. Although in conventional cosmological scenarios μ<1 necessarily leads to a universe that will grow infinitely old, this conclusion can be avoided in ways which are reasonably natural. One of these is to assume the existence of a small negative cosmological constant. Another way is to postulate the existence of unstable fields with a long time scale for the onset of the instability. An example is a scalar field with a negative squared mass and ¦m¦≲10⁻³²eV. Other examples include fields for which the instability is generated by quantum corrections in curved space-time. All of these are capable of halting the expansion of an open universe and forcing it to recollapse into a “big crunch.”