Acceleration of the Expansion and Dark Energy
Although we do not understand why the universe is expanding, we do know from General Relativity that
gravity should counter that expansion. This is because mass bends space-time, while space-time forms the
lattice through which masses move. Hence, mass and space-time are tied to each other. For this reason, it
is natural to expect that the expansion should have decelerated as the universe aged. It is actually possible
to determine directly whether this is the case.
When we observe distant galaxies, we are looking back in time, since the light that we detect left that
galaxy long before it reached us after traveling across space. If the expansion has been slowing down,
then the value of the slope of the velocity
vs
. distance graph should be higher at very large distances
corresponding to times closer to the beginning of the Big Bang. That is, if the rate of expansion were
higher in the past, the graph would curve up rather than remain a straight line. In this case, Hubble’s
“constant” would not really be constant.
Figure 11-7. The curvature of a sphere or circle is
only apparent when the radius is not many of orders
of magnitude larger than we can see. Note how the
section of the circle inside the square becomes
straighter as the radius of the circle increases.
According to current cosmological theory, Inflation
did the same to the universe, making space-time
very flat.

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Chapter 11: Big Bang Cosmology
11-10
Actually, when we observe extremely distant galaxies it is no longer convenient — or even correct — to
use velocity on the Hubble Law graph (Fig. 10-2). Rather, astronomers usually plot on the horizontal axis
the redshift
z
, which is defined in equation (10-3). One plus the redshift (1+
z
) (see eq. 10-2) corresponds
to how many times the universe has expanded since the light we now observe left the galaxy that emitted
it. For example, for a galaxy at a redshift
z
=3 (so 1+
z
= 4), the universe has expanded by 4 times during
the time it took for the light to travel from the galaxy to us. On the vertical axis astronomers often plot the
brightness of the object, which is the quantity that they measure when they determine the distance through
use of equation (6-2).
Figure 11-8 shows the graph of the brightness of a number of a certain type of exploding star called a
Type Ia supernova vs. redshift
z
. Although the data points are somewhat scattered in the crucial upper
right-hand corner, the observations agree better with the case in which the expansion of the universe is
accelerating
.
What could cause the expansion of the universe to accelerate? There must be some property of the
universe or some force that is stronger than the combined gravity of all the matter in the universe. Recall
from Chapter 10 that Einstein included such a property, which he called the Cosmological constant
, in
General Relativity. This would need to have strange properties to remain constant while the volume of the
universe increases. An alternative, nicknamed “ether,” is some hypothetical property of space that would