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C H A P T E R 7
e Future
7.1 THE FUTURE AT LARGE SCALES
Figure 7.1 shows the evolution of the universe for several different cosmological models. Unlike
Figure 6.1, this is not a Hubble diagram of velocity (or redshift) vs. distance. Rather it is a graph
of the relative scale factor of the universe plotted vs. time. e scale factor can be thought of as
the distance between two arbitrary co-moving observers—located on two galaxies distant from
each other, for example. As time passes, this distance increases, and the progression is a record
of the expansion of the universe.
e graph extends from the past, through the present (t D 0), through projections of the
future. e slope of the graph at the present, marked by “now,” is set by the Hubble constant. is
is observed to be about 70 km/s per megaparsec, and so it is fixed. us, all of the models shown
have the same slope at that point. If they did not, they would not agree with our measured value
of H
0
.
We observe the past, through the concept of look-back time. e future, on the other
hand, is a projection. If we apply a particular physical model to the expansion of the universe,
does it agree with what we observe of the past? And if so, what does that model predict about
the future?
Figure 7.1 shows five possibilities. e straight line marked
M
D 0 shows the conse-
quence of a model universe that has neither matter nor dark energy. Projected back to the big
bang, it gives an age that agrees well with our observations of the oldest objects in the universe.
But it disagrees with observation in other details. In particular, there quite obviously is matter
in the universe, and an accounting of both ordinary and dark matter indicates there is enough
to significantly alter the expansion of the universe.
e model marked
M
D 1 has some appeal, because it agrees better with estimates of
the total amount of both ordinary and dark matter. It has other agreeable qualities as well, as
we shall see later. But the age is wrong; it implies the universe is less than 10 billion years old.
And we have good evidence that the globular clusters, as just one example, are significantly older
than this.
Four of the five models expand infinitely into the future. But one—the one marked
M
D
6–eventually contracts. At about 5 billion years in the future the universe stops expanding and
then begins to contract, leading to the Big Crunch in about 18 billion years. is is an intriguing
idea, but it would require a density of matter many times greater than what is observed, even
when dark matter is taken into account.
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