Question

What is the best evidence that dark matter is "cold" (i.e., consists of particles whose thermal velocities are very small today)?

• A. The observed temperature of the cosmic microwave background is only 2.73 K, so the universe is cold today.

• B. Warmer dark matter would have been moving too quickly to form the dark matter halos of galaxies.

• C. The kinetic energy (energy of motion) of dark matter particles must be very low so that the rare collisions with ordinary matter in terrestrial dark-matter detectors leave no observable trace.

Answer 1

Option B is the best evidence.

The Lambda Cold dark matter (LCDM) theory predicts that dark matter should be cold.

It is intuitive that it is more difficult to form a gravitationally bound structure if the particles that form it move too fast. Lower thermal velocities of dark matter particles imply that structures can grow in size after they decouple from the radiation field, way before recombination. You can picture it like this:

There are primordial seed perturbations in the density field.If the DM particles are cold, they are slow so the these perturbations can start growing (once decoupled from expansion) even during the epoch in which baryons are still strongly coupled to radiation.Only after recombination, baryons are able to cool down, but at that point the seed perturbations are large enough to become potential wells (dark matter halos) to baryons to settle in (dark matter halos).

Then small halos merge together to form larger ones, and so on. The result is then galaxies form smaller, and grow by mergers. This is what we call the CDM galaxy formation model.

Now compare this to a case in which DM particles are hot. Since they diffuse (Silk Damping) easier, you need larger structures as seeds. So in this picture galaxies start large, and fragment over time.

Which is one do we observe? We just need to count galaxies, turns out that CDM works best.