Expert: Philip A. Stahl - 10/20/2011

Question
After viewing an episode of "trough the wormhole" I was left pondering about dark matter and dark energy.

Can't the continued expansion of the universe simply be explained through diffusion. Like dropping some ink in water, where the universe is the ink and the water is the "nothing" that surrounds it?

As the paricles of ink get further and further apart, the surface area would increase and so would the expansion and speed of the particles relative to one another.

Answer
Hello,

The problem with comparing the diffusion of ink spreading through water with the accelerating cosmic expansion, is that it is a false analogy.

In the case of ink diffusion, one beholds actual particles of ink diffusing through a confined medium (e.g. bowl of water.) In the case of cosmic expansion the "container" itself is expanding!  

To get an insight, we can examine the equation that underpins cosmic expansion and whether it is accelerated or not (cf. Perlmutter, Physics Today, 2003)

R’’/R = - 4π/ 3  G rho (1  +  3 w)

Here R is a cosmic scale factor, R’’ is the acceleration (e.g. second derivative of R with respect to time t), G is the Newtonian gravitational constant, rho is the mass density. We inquire what value w must have for there to be no acceleration or deceleration. Basic algebra shows that when w = -1/3 the whole right side becomes zero. The supernovae plot data constrain w such that it cannot have a value > (-1/2). Most plausibly, w (the ratio of pressure to density) is called the cosmological equation of state (Perlmutter, ibid.)

w = (p / rho) = -1

Specifically the term (rho + 3p) acts as a source of gravity in general relativity, (where rho = energy density).

If we set:  0 = (rho + 3p) then:

p =  -rho /3   (or  rho  = - 3p)

and if:  p <  (rho/3) we have gravity that repels

In other words, a gravitational repulsion may be the best agency to explain why the *cosmos* is accelerating - not merely the matter (or dark matter) within it.

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.

Again, we are not merely looking at the rates of relative displacements (dx/dt, dy/dt, dz/dt) between particles themselves but of aggregate space-time, i.e. the geometric manifold within which dark matter, dark anergy and ordinary matter are contained.

In other words, if your conjecture were valid there would be no term of R" in the expansion equation, where R is the *cosmic* scale factor!