Once matter and radiation were decoupled, gravity became the dominant influence
on the evolution of the universe. Density fluctuations (whose existence is confirmed
by irregularities—“ripples”—in the sea of 2.7-K radiation that were discovered in 1992)
led to the formation of the galaxies and stars that adorn the night sky. Early super-
novas spewed out the various elements heavier than helium that later became incor-
porated in other stars and in their satellite planets. Living things developed on at least
one of these planets, and quite possibly on a great many others as well, which brings
us to the present.13.9 THE FUTURE
“In my beginning is my end.” (T. S. Eliot, Four Quartets)Will the universe continue to expand forever? This depends on how much matter the
universe contains and on how fast it is expanding. There are three possibilities:1 If the average density of the universe is smaller than a certain critical density (^) c
that is a function of the expansion rate, the universe is openand the expansion will
never stop (Fig. 13.13). Eventually new galaxies and stars will cease to form and existing
ones will end up as black dwarfs, neutron stars, and black holes—an icy death.
2 If is greater than (^) c, the universe is closedand sooner or later gravity will stop
the expansion. The universe will then begin to contract. The progression of events will
be the reverse of those that took place after the Big Bang, with an ultimate Big Crunch—
a fiery death. And after that another Big Bang? If so, then the universe is cyclic, with
no beginning and no end.
3 If (^) c, the expansion will continue at an ever-decreasing rate but the universe
will not contract. In this case the universe is said to be flatbecause of the geometry
of space in such a universe (Fig. 13.14). If (^) c, space is negatively curved; a two-
dimensional analogy is a saddle. If (^) c, space is positively curved; a two-dimensional
analogy is the surface of a sphere. In all cases, however, spacetime is curved (Sec. 1.10).
Elementary Particles 501
Time
ρ = ρc
Open universe
Flat universe
Closed universe
Big Bang Big Crunch
Radius of the universe
ρ > ρc
ρ < ρc
Figure 13.13Three cosmological models that follow from the equations of general relativity. The quan-
tity is the average density of the universe and (^) c, the critical density, is in the neighborhood of
9 10 ^27 kg/m^3 , equivalent to about 5 hydrogen atoms per cubic meter.
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