Astronomy 162: Professor Barbara Ryden
Monday, March 10
THE ACCELERATING UNIVERSE
``This is the way the world ends,
Not with a bang but with a whimper.''
- T. S. Eliot
- Most of the density of the universe is contributed
by dark matter.
- The expansion of the universe currently seems to be speeding up.
- The acceleration of the expansion could be caused by a
(1) Most of the density of the universe is contributed by
As I was saying
last week, space
is curved on small scales by small massive objects such
as people, planets, stars, galaxies, clusters of galaxies,
and superclusters of clusters. On very large scales, however,
space seems to be flat. That is, it is neither positively
curved, like the 3-d equivalent of a sphere, nor negatively curved,
like the 3-d equivalent of a hyperboloid. Rather, it is the
3-d equivalent of a plane, and obeys all of Euclid's laws
of geometry. The laws of general relativity tell us that
for an expanding universe to be flat, its density must be
equal to a critical density which is proportional to the
square of the Hubble constant. For our universe, the
critical density is about 9 x 10-27 kilograms
per cubic meter. (This extraordinarily low density is equivalent
to taking the matter in a small drop of water and spreading
it over the volume of the Earth.)
Small though the critical density is, the amount of matter
in the universe seems to be still
smaller than the critical density.
The amount of matter clumped up into clusters and superclusters
only contributes about 30 percent of the critical density.
What provides the rest of the mass (or energy, since E = mc2)?
Photons provide energy, but all the photons in the universe,
from the Cosmic Microwave Background, from starlight, from
your computer screen, and from all other sources, provide
far less than one percent of the critical density. The
rest of the critical density is provided by some form
of energy (or mass, since m = E/c2) which
is smoothly distributed throughout the universe, instead
of being clumped up into clusters and superclusters.
This mysterious form of energy is called dark energy.
The name ``dark energy'' is something of a confession
of ignorance. Cosmologists could just as well have called it
``whatchamacallit''. What do we know about dark energy?
- Dark energy has a density of roughly 70 percent of
the critical density. (That is, a mass density of 6 x 10-27
kilograms per cubic meter or equivalently an energy
density of 6 x 10-10 joules per cubic meter.)
- Dark energy doesn't emit light (hence the name
(2) The expansion of the universe currently seems to be
The standard way of determining the properties of dark matter
is to look for its influence on luminous matter. A similar
analysis can be done of dark energy. In
particular, the dark energy strongly affects the expansion
of the universe. Remember, the universal expansion of the
universe causes galaxies to move away from each other. However,
galaxies have mass, and hence the mutual gravitational
attraction of the galaxies will tend to make the expansion
slow down. Now consider the effect of
adding dark energy to the universe. The energy
(or mass) of the dark energy will add more gravitational
attraction to the universe, and hence will tend to
amek the expansion slow down even more.
HOWEVER, if the dark energy has pressure
as well, the pressure could act to speed up
So, how do astronomers go about determining whether the
expansion of the universe is speeding up or slowing down?
The current rate of expansion is given by the Hubble constant
(H0). To find the Hubble constant, you can plot
the distance (d) of standard candles as a function of their
recession speed (v). If the resulting plot has a shallow
slope (that is, if galaxies with large recession speed have a relatively
small distance), then the universe is expanding rapidly and
H0 is large. By contrast, if the plot of distance
as a function of recession speed has a steep slope, then
the universe is expanding slowly and H0 is small.
But H0 tells us how rapidly the universe is
expanding now; how can we tell how rapidly the universe
was expanding in the past? Remember, ``a telescope is a
time machine''. The speed of an extremely distant galaxy
tells us how fast the universe was expanding
at the time the light we observe was emitted; that may have
been billions of years ago, when the universe was much younger
(and may have been expanding much faster or slower). If
a plot of distance as a function of recession speed has
a shallower slope at large recession speeds, then the
universe was expanding more rapidly in the past than it
is now. If a plot of distance versus recession speed is
steeper at large recession speeds, then the universe
was expanding more slowly in the past. (This verbal description,
I realize, may be a bit confusing; a look at
Figure 28-17 of
the textbook should make things clearer.)
During the past decade, research groups have carefully
observed Type Ia supernovae with large redshifts (and hence
at large distances). After observing dozens of distant
supernovae, they plotted the distances (deduced from
their apparent brightness) as a function of their
recession velocity (deduced from their redshift).
- Result: distant supernovae have redshifts slightly
smaller than they would if the expansion
of the universe were not accelerated.
- Deduction: the universe was expanding more slowly
in the past than it is now.
- Speculation: the speed-up of the expansion is caused
by the pressure of the dark energy.
(3) The acceleration of the universe might be caused by
a cosmological constant.
What could be the source of dark energy, the weird stuff
filling the universe and causing its expansion to speed up?
Actually, Albert Einstein had an answer to that question
as long ago as 1917, two years after he published his Theory
of General Relativity. In 1917, Edwin Hubble had not yet
discovered the Hubble Law; hence, Einstein assumed that
the universe was neither expanding nor contracting. This
was a problem, since Einstein knew that gravitational
attraction would make the universe collapse. Thus, he
was searching for a repulsive force that would exactly
balance the attractive force of gravity, and thus
leave the universe in equilibrium. What Einstein
did to ensure the equilibrium of the universe was
insert a ``fudge factor'' into the equations describing
gravity. This fudge factor was symbolized by the
Greek letter Lambda (I don't know why - maybe Einstein
picked that letter out of a hat), and was given
the name of the cosmological constant.
Einstein's cosmological constant, when inserted
into the equations of general relativity, provides:
Thus, the cosmological constant acts just the way
observations tell us that the ``dark energy'' behaves.
- an energy density (which flattens the universe)
- a pressure (which accelerates the expansion of the universe)
When Einstein first introduced the cosmological constant
in 1917, he regarded it as an
ugly mathematical contrivance. (He thought
it marred the elegant simplicity of his equations.)
When Hubble pointed out, a decade or so later, that
the universe was not static, Einstein
happily jettisoned the cosmological constant.
Now, however, the acceleration of the universe has
caused scientists to bring Einstein's cosmological
constant out of the attic and dust it off. Moreover,
where Einstein thought of the cosmological constant
as a purely mathematical ``fudge factor'', modern physicists
have found a physical reality behind it. The cosmological
constant, according to the laws of quantum mechanics,
could represent the energy and pressure of the vacuum.
In classical Newtonian physics, a vacuum is totally
empty, and thus can't have an energy or pressure. In
the world of quantum mechanics, however, vacuums are
not totally empty. In apparently empty space, pairs of
particles and antiparticles are constantly being
created, only to annihilate with each other a short
time later. Protons and anti-protons, neutrons and
anti-neutrons, electrons and anti-electrons (also
called positrons) - they are constantly popping out
of nowhere, only to be destroyed a tiny fraction of
a second later. These virtual pairs
of particles, as they are called, provide energy
and pressure during the short time of their existence.
Cosmologists have put together, within the broad
frame of the Big Bang Theory, a more specfic
model of the universe. The observations on
which the model is based:
The deduced properties of the model:
- The mass of clusters and superclusters (deduced from
the motions of galaxies within clusters and superclusters).
- The angular size of hot spots in the Cosmic Microwave Background.
- The recession speed of distant Type Ia supernovae.
Although the Big Bang Theory has been around for the
best part of a century, this specific model (flat yet accelerating)
is a relatively recent development. The details
(70 percent dark energy? 60 percent? 80 percent?)
are being vigorously debated by cosmologists.
- Matter (some of it luminous, some of it dark) provides
30 percent of the critical density.
- Dark energy (probably in the form of a cosmological
constant) provides 70 percent of the critical density.
- Space is flat (or very close to flat) on large scales.
- The expansion of the universe is speeding up; the
universe may have started with a Bang, but it looks like
it will end with a long-drawn-out Whimper.
Prof. Barbara Ryden
Updated: 2003 Mar 9
Copyright © 2003, Barbara Ryden