Dark Matter and Energy

1. Dark Matter and Energy

2. 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/Galaxy_rotation_problem

4. 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 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

5. Distant supernovae velocities • The latest survey of high-z type Ia supernovae came out just last month in Astrophysics656. 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.

6. 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. Acceleration of the universe and negative pressure

7. 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.

8. Cosmological term just what’s 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.

9. Observational conclusions • 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.

10. There it is; and yet… • What are dark matter’s ingredients? Viable options are elusive. • A very pushy candidate for dark energy exists and it is a terrible one.

11. 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.

12. 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.

13. 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:

14. 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).

15. Symmetry Breaking • 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 Ginzburg-Landau potential density. • As you will see, this broken symmetry also results in a cosmological constant term.

16. A Lagrangian density transformation

17. 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.

18. 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.

19. 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 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.