Describe some possible futures for the universe that scientists have come up with. what property of the universe determines which of these possibilities is the correct one?

If the cosmos emerged from the Big Bang with sufficiently high density, then it contains enough matter to halt its own expansion and the recession of galaxies will stop. Red shifts will turn to blue shifts as the universe begins collapsing inward and stars and planets and galaxies will collide with increasing frequency and violence as space diminishes. The entire universe will shrink towards a super dense, super hot singularity, much like the one from which it originated, the "big crunch".

Gravity of a low density universe will be too weak to half the present expansion. The universe will expand forever, the galaxies continually receding, their radiation steadily weakening with increasing distance.  

In time, we will see no galaxies in the sky beyond the Local Group. Eventually, the Local Group will peter out as their fuel supply is consumed. A "cold death" will happen whereby all radiation, matter, and life are eventually destined to freeze. This would take about a trillion years to happen.

The universe can expand forever, in which case we die a cold death in which all activity gradually fades away, or the expansion can stop and the universe will recollapse to a fiery Big Crunch.