Question

What is the difference between hot dark matter and cold dark matter? What difference does it make to cosmology?

Answer 1

Hot Dark Matter : Dark Matter moving at relativistic speeds.
Cold Dark Matter: Dark Matter moving at non-relativistic speeds.
They affect the way structures form in the Universe.

Explanation:

Depending on how a particle's kinetic energy compares with its rest mass energy, particles are classified into:

Non-relativistic: `E_k \lt\lt E_0`,
Relativistic : `E_k \approx E_0`,
Super-relativistic: `E_k \gt\gt E_0`;

HDM & CDM : If the dark-matter particles are relativistic or super-relativistic they are called Hot Dark Matter (HDM), otherwise they are called Cold Dark Matter (CDM).

Since Dark Matter has not been detected yet, Cosmologists can only speculate about the nature of Dark Matter - Is it hot or cold? The current consensus view is that it is cold for most part. Because if it were hot, then the structure formation theories predict that all structures smaller than massive galaxies would have been destroyed by a process called Free Streaming. Since we have structures smaller than galaxies we conclude that the Dark Matter cannot be predominantly hot. Though there could be little bit of hot dark matter mixed among predominantly cold matter.