Expert: Philip Stahl - 8/27/2006

Question
My interest in this is purley motivated by a biblical verse. To be excact, there is a verse in the Bible that says God lives in a light that no man has seen or can see.

I understand that our Universe is sorta expanding, and most dark matter is thought to be non-baryonic?

Could this dark matter be something of another dimension if its non-baryonic? An eternal and infinite dimension or power our universe is expanding into?

Any input on dark matter you can give me would be much appreciated.

Answer
Hello.

Most astronomers, based on current data (taken from plotting brightnesses of Type Ia supernovae vs. redshift, (See, e.g. 'Supernovae, Dark Energy and the Accelerating Univers'e, by Saul Perlmutter, in Physics Today, April, 2003, p. 53 and also the main article about Dark energy in the June, 2003 issue of ASTRONOMY magazine) believe that *dark energy* or vacuum energy is driving a more rapid rate of expansion for the universe.


The cosmological "equation of state" (think of something like the equation of state for an ideal gas, e.g. P = nkT) for this vacuum energy is:

w = (Pressure/ energy density) = -1

But, as Perlmutter and others note, whenever w < ( -1/2) we must have a condition of repulsive energy!

This is the primary feature of dark energy. That the matter affected is being mutually repelled - in total contradiction to the normal behavior of (attractive) gravitation- and this repulsion is accelerating the expansion of the cosmos.

This is consistent with Einstein's general theory of relativity - which one could say approaches the status of a 'basic law of physics'.  In this case,  a negative pressure  meshes with general relativity's allowance for a "repulsive gravity" - since any negative pressure has associated with it gravity that repels rather than attracts.

Some might argue that cosmic repulsion shows a "new law" of physics, but it's merely an extension of the existing concept of gravitation to show it has a repulsive as well as attractive aspect, and has always been consistent with Einstein's general theory of relativity. (Which, of course, posits a *four-dimensional* space-time)

Dark matter which you referenced, is not connected to this. Doesn't have to be, anyway. You see, dark matter can exist even in a cosmos with normal gravitation.

Astronomer Fritz Zwicky in 1933 actually laid the original, observational basis for dark matter. His measurements of galaxy clusters highlighted a 'missing mass'. He found that the mass needed to bind a cluster of galaxies together gravitationally was at least ten times the (estimated) apparent mass visible.

This mass, because it was inferred but not directly detectable, became the first dark matter. Around the same time there were other confirmations, based on observed stellar motions in the galactic plane, by Dutch astronomer Jan Oort. He determined there had to be at least three times the mass visibly present in order for stars not to escape the galaxy and fly off into space.

By the late 1970s, astronomers realized there were forms of matter that didn’t emit light. Among the most talked about candidates were black holes, marking the end stage of evolution for very massive stars. In the black hole, no light escapes and the mass is typically much greater than that of the Sun. One million black holes in the center of our galaxy (probably a conservative number) represents a lot of dark matter. Multiply that by billions of other galaxies, in similar scenarios, and one has an enormous store of dark matter. In fact, given the number of massive stars in our galaxy, it is likely that eventually, 90 percent or more of the stars will have collapsed into black holes, especially with currently accepted lower mass thresholds for black hole formation.

Dark matter itself occurs in either baryonic or non-baryonic forms, depending on whether it reacts with radiation or not. If not, it's non-baryonic. This non-baryonic matter further breaks down into 'cold dark matter' and 'hot dark matter'. The terms 'hot' and 'cold' not so much indicative of current temperatures but rather the phase of the early universe at which the particular dark matter 'decoupled'. (An earlier decoupling indicates a higher background temperature - since it's closer in time to the Big Bang).

The most widely studied example of 'hot dark matter' is the neutrino (of which there are a number of varieties, e.g. mu neutrino, tau neutrino, electron neutrino). Meanwhile, cold dark matter candidates include any magnetic monopoles that may exist, as well as primordial black holes (also called 'mini-black holes, made populace by Stephen Hawking), and gravitinos.

None of these requires any extra dimensions beyond the 4 dimensions of normal space-time.

The Boomerang and MAXIMA UV measurements to do with type Ia supernovae have led to the most recent assay for proportions of normal matter vis-a-vis dark matter and dark energy. (See, e.g. Physics Today, July, 2000, p. 17): Thus, we have:


7% - ordinary visible matter

93% - dark component, of which:

- 70% is DARK (vacuum) energy and
- 23% is dark matter


The particular dynamics and projections for future expansion depend on the nature of the cosmological models used as a template for expansion. In most case, these belong to the family of the F-R-W or Friedmann-Robertson-Walker cosmologies. (Of which deceleration is one subset of solutions, as is acceleration).

To fix ideas, one needs to obtain the curvature and also preferably the cosmic density.

Now, using a particular F-R-W template, one can have:

k = +1 (positive curvature - spherical geometry)

k = -1 (negative curvature - hyperbolic or horse saddle type geometry)

k = 0 (flat or Euclidean universe)

Universes that re-collapse (decelerate), expand forever with zero limiting velocity (e.g. v uniform) or expand forever with positive limiting velocity (accelerate) are called in turn: 'closed' (can be k = +1); 'critical' (k=0)or 'open' (can be k = -1), respectively.

Now, to determine whether any F-R-W cosmological template leads to deceleration or not, we need to find the cosmic density parameter:

Omega = rho / rho_c

where the denominator refers to the critical density. Thus if:

rho > rho_c

then the cosmic density is able to reverse the expansion (e.g. decelerate it) and conceivably usher in a new cycle. (New Big bang etc.) The observations that help determine how large rho is, come mainly from observing galaxy clusters in different directions in space and obtaining a density estimate from them.

Current data, e.g. from Boomerang and other satellite detectors suggest Omega ~ 0.3 or that:

rho = 0.3 (rho_c)

I.e. that rho < rho_c so there is no danger of the cosmos decelerating, and indeed the Type Ia supernova data shows the opposite, as noted earlier.

Note that none of the above discloses expansion into any "infinite" dimensions - and as I noted, non-baryonic matter exists in the same normal dimensional confines as baryonic matter. Nor does any data disclose an eternal expansion. So far as we know, at some point - perhaps 10^ 99 years into the future - all expansion must eventually stop. The cosmos will merely have expired in what is called 'heat death'.