Dark Matter and Energy

1
Dark Matter and Energy
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Some observations about the universe

• It would appear that there is more matter in the
  universe, called dark matter, than we see. We
  believe this because
• 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.

3
Galactic rotation rates

• 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.

Picture Source http//en.wikipedia.org/wiki/Galax
y_rotation_problem
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Relative helium mass

• 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 dont 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 httpastro.ucla.edu/wright/BBNA.h
tml
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Distant supernovae velocities

• 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 Hubbles 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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Acceleration of the universe and negative pressure

• In an isotropic and homogeneous universe, the
  general theory of relativity predicts that the
  acceleration of the universe will be
• This will only produce a positive acceleration
  if
• 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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Dark energy and the cosmological constant

• 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.

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Cosmological term just whats needed

• 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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Observational conclusions

• What we see is only a small amount of the
  universes 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 universes
  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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There it is and yet

• What are dark matters ingredients? Viable
  options are elusive.
• A very pushy candidate for dark energy exists and
  it is a terrible one.

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Dark matter is not made of

• 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.

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Dark energy candidate vacuum energy

• 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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Solution to vacuum energy dilemma
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
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A possible source of dark matter and energy

• 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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Symmetry Breaking

• The Ginzburg-Landau potential density has two
  minima.
• At high temperatures, the systems 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
  Ginzburg-Landau potential density.
• As you will see, this broken symmetry also
  results in a cosmological constant term.

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A Lagrangian density transformation
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Remove references to s

• 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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Implications

• 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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Conclusion

• 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 Einsteins field equations.
• Finding out what these materials are had been
  troublesome since the standard model of quantum
  mechanics doesnt 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.