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On Wikipedia, it says

In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. According to the current standard model of cosmology, Lambda-CDM model, approximately 27% of the universe is dark matter and 68% is dark energy, with only a small fraction being the ordinary baryonic matter that composes stars, planets, and living organisms. Cold refers to the fact that the dark matter moves slowly compared to the speed of light, giving it a vanishing equation of state. Dark indicates that it interacts very weakly with ordinary matter and electromagnetic radiation. Proposed candidates for CDM include weakly interacting massive particles, primordial black holes, and axions.

Why is "Cold" defined like this? (see the bolded sentence.) What is the true meaning of "Cold"?

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  • $\begingroup$ Welcome to Physics. Please don't post screenshots of text; instead, copy and paste it into your questions, and link to the pages you're quoting. I'll edit things appropriately this time so that you can see how it should be done. $\endgroup$
    – Michael Seifert
    Commented May 21 at 17:12
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    $\begingroup$ Low energy = cold. $\endgroup$
    – Jon Custer
    Commented May 21 at 17:14
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    $\begingroup$ FWIW, I think that Wikipedia is being a bit generous in this definition. As the term cold dark matter is used in the context of the Lambda-CDM model, not everyone would include axion dark matter within that definition. Many people would limit CDM in this model to about 1 keV or more of mass per particle and would require that it be "very nearly" collisionless. Axion-like dark matter candidates are much less massive and are not always collisionless in the sense of that the LambdaCDM model uses that term. $\endgroup$
    – ohwilleke
    Commented May 22 at 1:43
  • $\begingroup$ @ohwilleke Mass $\gg$ keV is for particles that were in thermal contact with the radiation at some point, since that leads to a connection between mass and velocity distribution. Axions would have never been in thermal contact, so they can be cold despite being light. I think most people would describe QCD axions (mass $\gtrsim 10^{-5}$ eV) as cold dark matter. Ultralight axion-like particles (mass $\lesssim 10^{-20}$ eV) are more questionable, since even without initial thermal motion, they suppress small-scale density variations for other reasons. $\endgroup$
    – Sten
    Commented May 22 at 2:03
  • $\begingroup$ @Sten Fair point. But QCD axions aren't very strong DM candidates, unlike much lighter axion-like particles. $\endgroup$
    – ohwilleke
    Commented May 22 at 2:25

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What is the meaning of "cold" in cold dark matter?

It is a description of the velocity distribution of the dark matter at very early times, before any complicated structures like galaxies have formed. The idea is that at these times, at each point in space, there are dark matter particles with a spread of velocities. For cold dark matter, that spread is very narrow.

This is important because it affects the formation of structure later on. In the Universe's initial conditions, there are minute variations in the density, at a level of about one part in 10-100 thousand ($10^{-4}$ to $10^{-5}$). Over time, these density variations are amplified by gravity, because regions of excess density tend to pull in material from their surroundings. These initial variations appear to exist at all scales. At large scales, they seed galaxies and galaxy clusters.

If the dark matter is not cold, then the velocities of the dark matter particles tend to blur out small-scale density variations over time. These variations cannot persist on scales smaller than the distance that particles randomly drift. This could lead to consequences like a reduced abundance of small dwarf galaxies.

How does this relate to a "vanishing equation of state"?

This is related to the description of dark matter as a perfect fluid with pressure $p=w\rho$, where $\rho$ is the energy density and $w$ is the equation of state parameter. The expression "$p=w\rho$" is the equation of state. For ultrarelativistic particles (with near-light-speed random motions), $w=1/3$ in the perfect fluid approximation. With no random motion, $w=0$, so the equation of state vanishes.

Note that a fluid is, by definition, a system in which particles cannot pass other particles. In a fluid, all particles at a given point move coherently; there is no spread in velocities. This is fundamentally an inappropriate description of dark matter, since dark matter particles can freely pass other particles. The perfect fluid description can work for dark matter at very large scales, e.g. when modeling the expansion of the Universe. However, it is not a good description at any scale for which the distinction between cold and non-cold dark matter is relevant.

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  • $\begingroup$ So can I understand“cold” as having almost no macroscopic thermal motion and therefore no thermodynamic temperature? Do they only affect surrounding matter through gravitational interactions? $\endgroup$
    – luckchen jammy
    Commented May 22 at 5:26
  • $\begingroup$ @luckchenjammy Yeah, essentially no thermal motion, and therefore a temperature close to 0. Note however that this is only at early times. Dark matter in galaxies can be quite hot, because it picks up energy during infall, and this is independent of whether the dark matter is "cold dark matter". Regarding the second question, dark matter has no known nongravitational interaction, so indeed it might only affect surrounding matter gravitationally. $\endgroup$
    – Sten
    Commented May 22 at 5:46
  • $\begingroup$ For particle dark matter, there would be essentially no gravitational energy exchange between individual particles, so no temperature equalization. Temperature equalization is possible through gravitational collisions, but the rate scales inversely with particle mass and would be negligible for elementary particles (or indeed anything much lighter than a star). $\endgroup$
    – Sten
    Commented May 22 at 5:54

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