# Dark Matter

## Main Question or Discussion Point

Is it true that, if there was enough dark matter in the universe it could stop the expansion of it?
If it is, can someone explain to me how?

nicksauce
Homework Helper
Well, roughly, speaking, yes.

In general the universe can have one of three topologies. (see http://en.wikipedia.org/wiki/Shape_of_the_Universe). Either the universe is below the critical density and will expand forever (this is called an open universe), or the universe is at the critical density and will expand forever (this is called a flat universe), or the universe is above the critical density and will eventually stop collapsing and start contracting (this is called a closed universe). Observations indicate that the universe is very close to being flat.

So in principle, if there was more dark matter in the universe, so that the density was more than the critical density, it would eventually stop expanding. However, the same effect could be had by adding more dark energy, or more regular matter.

PhilKravitz
or the universe is at the critical density and will expand forever (this is called a flat universe)
Would it be correct to say that in a flat universe the expansion rate decreases asymptotically and that the size of the universe increases asymptotically never exceeding a certain size?

Dark energy dominates the energy density and put that kind of matter/energy content into Einstein's Equations and you get an accelerating universe.
Cosmologists estimate that the acceleration began roughly 5 billion years ago.

nicksauce
Homework Helper
Would it be correct to say that in a flat universe the expansion rate decreases asymptotically and that the size of the universe increases asymptotically never exceeding a certain size?
From the Friedmann equations, the expansion rate is

$$H^2 = H_0^2\left( \Omega_M(a^{-3}) + \Omega_{\Lambda}\right)$$

So in a flat universe the expansion rate asymptotes to $$H_0\sqrt{\Omega_{\Lambda}}$$.

The proper size of the observable universe is given by

$$R = \frac{a}{H_0}\int\frac{da}{a^2\sqrt{\Omega_Ma^{-3}+\Omega_{\Lambda}}}$$

So if there is dark energy, then this will asymptotes to a finite value, but if there is no dark energy, then it will be unbounded.