Sky and Telescope - May 2018 - 16

Runaway Cosmos

As odd as it sounds, the cosmic expansion rate
is not a speed. It's a time scale: the time it takes
the universe to double in size. In an accelerating
universe, this time shortens as cosmic history moves
forward. For example, say a universe doubles its size
in 10 billion years. Its next doubling might take only
8 billion years, and the one after that, 5 billion years.
That's what we mean by cosmic acceleration.

16

M AY 2 0 1 8 * S K Y & T E L E S C O P E

H
c
G
ρ
k
Λ
a

=
=
=
=
=
=
=

8πG
ρ -
3

kc2
+
a2

Λ
3

Hubble parameter
speed of light
gravitational constant
matter density of the universe
curvature of the universe
cosmological constant
size of the universe

p THE FRIEDMANN EQUATION Depending on how you define your
terms, there are several ways to write the equation that describes the
evolution of the universe, called the Friedmann equation. This version explicitly relates the expansion rate H to the matter density, the universe's
geometry (probably flat), and a cosmological constant.

contraction. But it had no real scientific rationale; it was a
fudge factor, a mathematical cheat to force his equations to
describe the steady, static universe he thought must exist.
When Hubble discovered the universe was expanding, Einstein saw no need for the constant anymore.
But the discovery of dark energy revived it. "Until that
time, the idea that there was a cosmological constant wasn't
something that was particularly viewed with a lot of support in the community," Freedman says. If something were
pushing the cosmos apart, then an antigravity force like the
cosmological constant - with the opposite effect Einstein
envisioned - might fit the bill.

The Energy of Nothing
If cosmic acceleration is constant, dark energy's origins may
be spacetime itself. According to quantum mechanics, even
a vacuum isn't empty. Virtual particles burst into and out of
existence, together generating an ubiquitous vacuum energy.
The existence of this energy has been confirmed in various
experiments, such as in the Casimir effect, in which two
uncharged plates in a vacuum still feel a force between them.
According to general relativity, any kind of stuff - matter
or energy - bends spacetime. Most things you're used to, like
people, planets, and stars, warp spacetime in a way that we
experience as gravity. Vacuum energy obeys the same spacecurving rule, but it has the opposite effect. This energy is an
intrinsic property of space itself, so the expansion of space
creates more of it. But you don't get it for free. Creating the
energy takes work. The result, it turns out, is that the vacuum
energy curves spacetime in a way that's opposite to what
normal matter and energy do. That opposite effect manifests
itself as antigravity.
As space expands and spawns yet more space, it comes
with a proportionate amount of vacuum energy. "If space
is empty and you expand it, it's not any more empty than it

N ASA'S GODDA RD SPACE FLIG H T CEN TER CONCEPT UA L IM AG E L A B

The Expansion Rate

H2 =

Dark
energy

{

If astronomers know anything about dark energy, it's that
the acceleration it powers is happening. The original, NobelPrize-winning discovery relied on comparisons between how
bright distant supernovae appear to be with how bright they
actually are, based on theories for how such stars explode.
These measurements enabled astronomers to determine cosmic distances with newfound precision.
The teams also determined how fast the supernovae's
galaxies were receding from us by measuring how much
cosmic expansion has stretched, and therefore reddened, the
light from its initial wavelengths. When they combined the
distance and redshift observations, the teams found that for a
given redshift, a galaxy was farther away than they expected
it to be - farther, even, than it would be if the universe
were totally empty, with no matter to slow down its expansion. Since the universe isn't empty, the result suggested that
expansion is actually faster now than in the past.
Other astronomers have since confirmed the observations,
measuring more supernovae and other sources with increasing precision. Data from the cosmic microwave background,
the afterglow of the Big Bang, also match cosmological
models that include dark energy. So do initial results from the
Dark Energy Survey, which probes how matter is distributed
in the universe and thus how dark energy has wielded influence on cosmic structure over time. The cosmos seems to be
ballooning at a greater and greater rate, and it's been doing so
for the last several billion years.
Observations do show that the expansion actually did
decelerate during the first half of cosmic history, when the
universe was smaller and matter and its gravity dominated.
But then dark energy took over and has ruled ever since. All
the data suggest the acceleration it produces is constant,
an intriguing property that traces back directly to Einstein.
When applying his theory of general relativity to cosmology,
Einstein realized his equations implied the cosmos doesn't
stay still. Presumably, due to the attractive pull of matter's
gravity, it was shrinking. He deemed that preposterous. So
he introduced a term, later dubbed the cosmological constant,
which represented an antigravity force that countered the

Geometry

{

Matter
density

Einstein Revisited



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