What Wi Ultimately Become of the Universe? 227
during the 1980s and 1990s, observations of cosmic background radiation and Type Ia
supernovas in very distant galaxies (which also means the galaxies were formed relatively
shortly after the Big Bang) showed cosmologists that not only was the universe expanding,
but that the expansion was accelerating! This ran counter to the widely accepted belief that
the expansion was slowing down. Some kind of energy source was required to account for
this increasingly rapid expansion. As a result, it made sense to reincorporate the cosmologi-
cal constant into the relativistic equations of gravity.
If these observations are correct, then the biggest blunder of Einsteins life may actually
have been that he ended up refuting his own cosmological constant. If Einstein had declared
that the cosmological constant was absolutely necessary, he might be even more renowned
as a genius.
The Mystery of Dark Energy
So what’s causing the universe to expand faster and faster? It could be that Einsteins idea
of the cosmological constant is correct, meaning that some constant repulsive force is accel-
erating the expansion of the universe. One explanation for this is that the very vacuum of
empty space has some energy that drives the acceleration. Astronomers call this unknown
energy dark energy. That energy may well be the cosmological constant (denoted with the
Greek letter lambda, L).
By observing distant supernovas, astronomers have been able to look back in time and
discover that the universe is acting as predicted in the models in Figure 5-7. In each model,
the gravity exerted by galaxies slows the universes expansion early in its life. This happens
because the galaxies are close together, so the gravitational pull they exert on each other
is very strong. This makes it difficult for them to move away from each other, thus slow-
ing the universes expansion. The gravitational pull among galaxies is so strong that even
though dark energy existed in the early universe and was trying to drive the galaxies apart,
it couldn’t completely overcome the force of their gravity. But eventually, the galaxies moved
far enough apart that their gravitational pull was weakened to a point at which the effect of
dark energy began to exceed the gravitational pull. At this point, the dark energy began to
drive the galaxies even farther apart, thus expanding the universe at an accelerated rate.
What Will Ultimately Become of the Universe?
The universe seems to be changing dynamically, after all. So what will ultimately happen to
the universe after a great deal of time passes? First, we have to know what kind of universe
we live in, because the type of universe we live in will tell us its eventual fate.
We will consider the Friedmann-Lemaitre-Robertson-Walker (FLRW) model of the
universe, in which the theory of the Belgian astrophysicist Georges Lemaitre (1894–1966),
who was also one of the advocates of the theory of cosmic expansion, is added to Fried-
manns three models of the universe that we looked at earlier. However, a little background
knowledge is required first.
The story is simple—the fate of the universe depends on the curvature of space, and
that curvature has a one-to-one correspondence with the average density r
m
of matter that
currently exists in the universe (the Greek letter rho, r, is used as the symbol for density).
The average density of matter in the universe that would be needed to halt the expansion of
the universe at some point in the future is called the critical density, or r
c
. To determine the
curvature of space, researchers often use the equation W
M
= r
m
/ r
c
, which is the ratio of

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