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Brian Good
Prof. Caraher
Phys. 197A
16 December 2010
The Mystery of Dark Energy and the Cosmological Constant
The expansion of the universe has always been an interesting point of
research for physicists. The observation that the universe is expanding was critical
in our current understanding of it, and was a revolution which led to inflationary
theories and the idea of the Big Bang. Discoveries in the early 1900s spawned
various theories about the state of the universe, some of which predicted a static
universe and some of which implied that it would eventually collapse in a “Big
Crunch.” However, all of these beliefs were turned on their head when scientists
discovered in 1998 that the expansion is actually accelerating outward. Searching
for an explanation for this phenomenon, physicists developed a theory of “dark
energy,” previously undetected energy responsible for this outward repulsion of the
universe.
From the days of Aristotle all the way until the 20th century, the universe was
thought to be static, neither expanding nor contracting. Even Einstein “could not
imagine the universe as anything but eternal and immutable” (Smolin 151). When
Einstein developed the general theory of relativity in 1915, the theory predicted,
contrary to widely held belief, that the universe would either expand or contract.
Einstein, a firm believer in the static universe, took this to mean that his theory
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needed revision. To reconcile this theory with the idea of a static and eternal
universe, he added a “cosmological constant” to the equation. This constant, if
positive, would act in a manner which would cause accelerating inflation of the
universe, opposite to the internal pull of gravitation. However, Edwin Hubble later
observed the universe to be expanding, and Einstein discarded his cosmological
constant as his “greatest blunder” (Smolin 151-152). Apart from the fact that the
theory of a static universe was wrong, Einstein’s cosmological constant was
unstable. A very minor fluctuation would cause the universe to either expand or
contract, an effect like balancing a pencil on its point, according to Russian
cosmologist and mathematician Alexander Friedmann. The balance between the
constant and the gravitational pull of matter would be only momentary. Based on
this problem, Friedmann developed what came to be known as the Big Bang theory,
which described an expanding universe, a model which Hubble’s observations soon
confirmed (“WMAP- Cosmological Constant or Dark Energy”).
However, as quantum theory developed, physicists began to realize that the
cosmological constant could not be ignored; quantum mechanics actually predicted
an enormous constant.
The Heisenberg uncertainty principle states that it is
impossible to measure the exact momentum and position of a particle. This implies
that nothing can ever be exactly still because this would require having a definite
momentum and position. Therefore, there must always be some movement, even at
the lowest possible temperature, and thus there exists a certain background energy
permeating the universe. The energy inherent to any particle, no matter its
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condition, is known as the vacuum or ground-state energy. Quantum theory implies
that any field will have a huge vacuum energy, so the gravitational fields in
Einstein’s general theory of relativity would have a huge cosmological constant
(Smolin 152). In fact, the constant predicted by quantum field theory is much too
big given the observed values, by a factor of about 120 orders of magnitude. It is
clear that while quantum theory allows for the existence of an “anti-gravity”
existence, it is not sufficient to correctly explain it (Schewe, Stein, and Castelvecchi).
In 1998, astronomers made a startling observation by studying the redshifts
of supernovas in distant galaxies: the expansion of the universe is actually
accelerating (Smolin 154)! This brought new possibilities to the idea of Einstein’s
cosmological constant, and it required a new way of thinking regarding the
universe’s composition. If the attractive gravitational force of all matter in the
universe is acting inward, there must be some undetected force countering this and
creating a net outward force. This mysterious entity became known as dark energy,
and it is currently believed to comprise roughly 70 percent of the universe (Smolin
15-16). So, the question is: where does this energy come from?
Albert Einstein was the first person to describe space as not a constant, static
field of nothing, but rather as a dynamic and malleable entity with definite
properties. The general theory of relativity detailed how matter can influence space,
as gravitational fields warp space. One property of space theorized by Einstein is
that it is possible for more of it to be created. When he invented the concept of the
cosmological constant, this constant was thought to be a property of
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space itself; therefore, the creation of more space would mean the creation of more
background energy, while no new mass was created. The ratio of energy to mass
would thus increase, causing a faster and faster outward expansion (Dark Energy,
Dark Matter). So, upon recognition that the universe is indeed expanding in this
fashion, one theory that could describe dark energy is that it is a form of
cosmological constant, and Einstein was not so far off after all. Instead of trying to
balance the cosmological constant with the effects of gravity, the theory might need
a larger constant which predicts the acceleration that has been observed; the
observed cosmological constant is not zero, but positive. A simple change in the
magnitude of the constant could possibly be all that is needed to correct Einstein’s
“blunder.”
Another possible explanation of dark energy is the theory of quintessence, or
a previously unknown type of energy field which pushes particles apart stronger
than any of the four fundamental forces can pull them together. As opposed to the
cosmological constant, quintessence provides a variable energy and force
dependent on the variation of space. Explained by cosmologist Paul Steinhardt,
"The cosmological constant is a very specific form of energy, a vacuum energy.
Quintessence encompasses a wide class of possibilities. It is a dynamic, timeevolving and spatially dependent form of energy with negative pressure sufficient to
drive the accelerating expansion."
The energy represented by the cosmological
constant has uniform properties, independent of the reference frame of an observer
moving through space and time; now matter where, when, or how it is measured, it
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always has the same value. Since the cosmological constant is constant through
time as well as space, it would have been the same in the earliest stages of the
universe as it is today, and it would have affected the universe in ways which could
have prevented the creation of the cosmos, as well as life on earth, as we know it. If
quintessence is real, it was negligible for the first five billion years of the universe,
only after which time the expansion truly accelerated.
Its strength adapts to
universal inflation, which would solve the problem of dark energy having an effect
on the early universe (Wanjek).
It is also possible that “dark energy” does not really exist at all, but is rather
the result of an unknown property of space, or part of an existing theory that is
misinterpreted. For instance, there is a chance that Einstein’s theory of gravitation
as described in his general theory of relativity could need revised beyond simply a
change in the cosmological constant. The new theory of gravity could contain
explanations of why space accelerates outward in terms of gravitational fields, and
would possibly allow for extra dimensions. This is one topic addressed by string
theory, which proposes the idea of several hidden dimensions which are “curled up”
and beyond the power of human observation. One or more of these dimensions
might cause the apparent accelerating expansion of three-dimensional space (“What
might Dark Energy be?”). The way in which the extra dimensions are compacted or
curled up could modify the actions of gravity. Thus, the nature of the expansion
would not be caused by some mysterious new energy, but rather by the principles
which govern spacetime itself. The cosmological constant could be a way to relate
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our three-dimensional observations to a potentially eleven-dimensional universe.
There are a plethora of string theories which coincide with the observation of a
positive cosmological constant (about 10500) (Smolin 158).
Initially, the theories
only allowed for a negative or zero constant, but in the 1990s, Joseph Polchinski and
Raphael Bousso developed a way to achieve string theories with positive
cosmological constants, consistent with observation (Smolin 155-156).
String theory might not be the answer, and perhaps general relativity simply
does not apply on extremely large scales. Einstein’s theory was proven on the scale
of our solar system, but there have been no experiments to prove that it holds true
on the scale of entire galaxies (Smolin 15). Newton’s law of gravitation needed to be
revised to give way to the general theory of relativity, so there could be aspects of
gravity still to be discovered, whether they act in extra dimensions or not. The
existence of an actual “dark energy” has not been proven; all we see are the effects
(Smolin 150).
The concept of dark energy is a relatively very recent one, and it is a puzzling
thought to physicists.
There are different possible explanations for the
phenomenon of the universe’s acceleration, some describing an actual energy
presence, and others simply calling for the rewriting of existing theories. Dark
energy could be an inherent energy of space, a completely new form of energy, a
revision to the theory of gravitation, or the manifestation of extra dimensions as
described by string theory. Perhaps it is none of these things, and the correct theory
is yet to be proposed. If dark energy does not exist, there are severe shortcomings
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in our current understanding of the behavior of the universe. Whatever is causing
the acceleration of expansion, it is clearly a sign of a major change in the way we
observe space.
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Works Cited
Smolin, Lee. The Trouble With Physics. New York: Houghton Mifflin Company,
2006.
“Dark Energy, Dark Matter.” NASA Science. 15 Dec. 2010
<http://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy>.
“WMAP- Cosmological Constant or Dark Energy.” NASA. 15 Dec. 2010
<http://map.gsfc.nasa.gov/universe/uni_accel.html>.
Wanjek, Christopher. “Quintessence, accelerating the Universe?” 16 Dec. 2010
<http://www.astronomytoday.com/cosmology/quintessence.html>
Shewe, Phil, Ben Stein and Davide Castelvecchi. “Can String Theory Explain Dark
Energy?” 2006. 16 Dec. 2010 <http://www.aip.org/pnu/2006/split/7812.html>
“What might Dark Energy be?” Universe Forum. 16 Dec. 2010
<http://www.aip.org/pnu/2006/split/781-2.html>