Originally posted as an answer to a question on the BAUT forum .
This week on the Astronomy Cast podcast the topic was galaxy formation. Apparently, before the luminous (baryonic) galaxies coalesced under gravity, the non-baryonic dark matter had already begun collecting into large structures that eventually formed the scaffolding for the galaxies. As I understand it, so-called dark matter is affected by gravity but does not interact with light (except to alter its trajectory by bending spacetime).
Here is my question: If dark matter is affected by gravity (and exerts its own gravitational pull, or bends spacetime in the same way and to the same extent as baryonic matter of equal mass), then shouldn't we expect to find dark matter in the middle of large gravity wells of baryonic matter? Shouldn't the dark matter and the regular matter "fall down the same holes"?
There's an important difference between ordinary matter and the dark matter, which is a consequence of the fact you already mentioned. Since dark matter doesn't interact with light, it cannot radiate away energy easily. In a cloud of ordinary gas, the individual atoms are flying every which way. When two atoms pass close to one another, they interact via (mainly) electromagnetic forces. One atom may bump into the other, shoving it and increasing its speed; or the first may slow the second down. The collision may excite one atom into a higher energy state, and then, after some period of time, that excited atom may emit a photon and return to its original energy state.
These interactions between atoms can dissipate both energy and angular momentum. Over a long period of time, a big cloud of gas may collapse into a rotating disk under the influence of its own gravity; after more time, the inner regions of a disk may collapse into a star.
Dark matter particles, on the other hand, do not interact with each other -- or with ordinary atoms -- in the same way. Their only (or main) type of interaction is gravitational. As a result, dark matter particles cannot lose energy or angular momentum via numerous little collisions and near collisions ... and so a big cloud of dark matter will not collapse and shrink to a much smaller size.
Here's an analogy: imagine a smooth road which dips down into a streambed and then rises out of it. That road will represent a gravitational potential well. Place an ordinary tennis ball on the road at the top of the dip. The ball will roll down the slope, across the bottom, then start to roll up the other side. However, because it loses a little bit of its energy to friction as it rolls, it won't make it all the way back up the other side; instead, it will roll back down, across the bottom, and back towards you. But it won't make it up your side, either. It will oscillate back and forth across the streambed, losing some energy each time, until it comes to rest in the middle of the streambed. That tennis ball is like ordinary matter: it eventually settles down into the middle of a gravitational well.
Dark matter, on the other hand, might be represented by a levitating object -- sort of like an air-hockey puck -- which can slide above the surface of the road without any friction at all. If you release it from the top of your side of the streambed, it will slide down the slope, across the streambed, and up the other side ... all the way to the top. It will _not_ lose any energy, and it will _not_ eventually settle in the middle of the streambed.