Transcript Dark Matter and Energy: An Overview and Possible Solution

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It would appear that there is more matter in the
universe, called dark matter, than we see. We
believe this because
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The edges of galaxies are rotating faster than we would
expect.
Between 23% and 25% of the visible mass of the universe
is helium.
Worse, it would appear that some of this
material, has a negative pressure. We
distinguish this from the more mundane dark
matter by calling it dark energy. We infer its
existence from the recession of distant
supernova.
We would expect galactic
rotation curves to look
like curve A, but find
they look like B.
 This could be accounted
for if there was a “halo”
of unseen matter
surrounding the galaxies.
 These rotation rates were
the original motivation
for suggesting the
existence of dark matter.
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Picture Source: http://en.wikipedia.org/wiki/Galaxy_rotation_problem
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Nucleosynthesis calculations show that
the amount of helium in the universe
depends of the density of baryons (the
nucleons and heavier particles that
constitute the bulk of the matter we
observe).
The relative helium mass is consistent
with about 7% of the universe, by
mass, consisting of baryons.
Therefore most of the universe must
consist of the stuff we don’t see and
at least some of that invisible stuff
must be dark matter.
As it turns out, dark matter will not
account for this discrepancy alone…
Picture Source: http:astro.ucla.edu/~wright/BBNA.html
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The latest survey of high-z type Ia
supernovae came out just last
month in Astrophysics 656. This
latest survey confirms that distant
supernovae are receding faster
than Hubble’s law would predict.
The slope in this graph of scaled
recession velocity versus scaled
distance indicates that the
universe is accelerating.
This implies some substance exists
with a negative pressure.
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In an isotropic and homogeneous universe, the general
theory of relativity predicts that the acceleration of the
universe will be
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This will only produce a positive acceleration if
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So, in addition to dark matter that must exist to
account for the galactic rotation curves, there must be
another substance that exerts a high negative pressure,
called dark energy.
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In principle, any material with a
negative pressure that overcomes
its energy density can serve as a
candidate for dark energy.
In practice, the measured
acceleration favors that produced
by the cosmological constant,
where the energy density and
pressure are equal in magnitude
and opposite in sign.
The cosmological constant comes
from removing the constraint
originally imposed by Einstein that
his field equations reduce to a
Newtonian inverse-distance
potential in the weak-field
approximation.
The cosmological
constant term in the
field equations behaves
like a perfect fluid with
a negative pressure
equal in magnitude to
its energy density.
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What we see is only a small amount of the universe’s essence.
The relative amount of baryons is fixed by the helium abundance. The
amount of the other types of matter can be determined by jiggling
numbers until we get a match with the universe’s acceleration:
Approximately 21% by mass of the universe is an electrically neutral (“dark”)
substance that is not made of baryons.
 Another 72% or so of the universe is a magic substance with negative pressure
described by the cosmological constant.
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 What
are dark matter’s ingredients? Viable
options are elusive.
 A very pushy candidate for dark energy exists
and it is a terrible one.
 Neutrinos
because they are relativistic and
would not collect within galaxies.
 Weakly Interacting Massive Particles (WIMPs)
because we expect they would cause galactic
cores to be denser than we observe.
Quantum mechanics
predicts that a Planck
energy density permeates
space.
 This energy density could
produce the effects seen
by “cosmological
constant goop.”
 Boy oh boy, does it
produce effects.
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This is energy density
taking place at the Planck
level, where quantum
gravitational effects should
become dominant. We
know exactly this much
about quantum gravity: 0.
Perhaps something
wonderful and magical
takes place at that level.
Translation:
Doctors Silverman and Mallett have proposed
that the dark matter and energy problems might
be solved by postulating the existence of a scalar
field that only interacts gravitationally and
whose self-interaction is described by a
Ginzburg-Landau potential density.
 Such a field would lose its symmetry from
gravitational interaction with other particles,
producing a cosmological constant and bosons
with extraordinarily small masses.
 These bosons would form a Bose-Einstein
condensate under present conditions, which they
call WIDGET (Weakly Interactive Degenerate
Ether).
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The Ginzburg-Landau potential density
has two minima.
At high temperatures, the system’s
average field will be zero and it will
sit on the top of the little hill at the
origin. Nothing particularly
noteworthy is happening at this point.
However, when the temperature
drops, the system will fall into one of
the two potential density wells,
breaking its symmetry.
The system will then oscillate about
this minimum, which we observe as a
particle with a mass related to the
quadratic coefficient in the GinzburgLandau potential density.
As you will see, this broken symmetry
also results in a cosmological constant
term.
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The self-interaction terms in y
have inverse powers of s in
them.
Silverman and Mallett worked
with the assumption that the
only medium of interaction for
this field is gravitational.
This implies that s is a
coupling constant related to
the relativistic gravitational
coupling constant, k.
They then made the simplest
substitution of s = 1 / k.
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The original scalar field has
produced a probability-density
field obeying the Klein-Gordan
equation, i.e., a boson.
The leftover term is actually a
cosmological constant term, which
becomes apparent when
examining the action.
Silverman and Mallett used the
relationship between the
cosmological constant and the
mass of the bosons to determine
that these bosons, if they exist,
would be the smallest massive
particles in existence.
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Cosmological observations and theory reveal the presence
of dark matter, which consists of neutral particles which
are not baryons, and dark energy, which is the result of the
cosmological term in Einstein’s field equations.
Finding out what these materials are had been
troublesome since the standard model of quantum
mechanics doesn’t supply the non-relativistic particles
needed for dark matter and since quantum field theory
predicts the presence of dark energy so strong it would
blow the universe to pieces.
Doctors Silverman and Mallett have presented one
alternative, which consists of the bosons that would be
produced from the broken symmetry of a scalar field that
only interacts gravitationally. These particles have very
small masses and the process that produces them also
produces dark energy.