I believe you may be referring to the words, "the energy-momentum tensor has the same form as the energy-momentum tensor of matter whose equation of state is p = ρ. The energy density of such matter rapidly decreases as the universe expands ..." in Linde's book.

In cosmology, it is helpful to characterize matter using the "equation of state" given by w = p / ρ. In this characterization, "dust" (which is pressure- and collisionless) has the equation of state w = 0; "normal" matter (nonrelativistic gas) would be 0 < w

Dear Toth,

Could you explain what "dust" exactly means in these cosmological situations? What is "Dust" made of?

Regards,

Rajat

Dear Rajat,

Dust is a non-relativistic matter. More exactly, one believes that particles  interact with each other only gravitationally in as dust.  Dust models are often employed in cosmology as models of a toy universe, in which the dust particles are considered as highly idealized models of galaxies, clusters, or superclusters.  In astrophysics, dust solutions have been employed as models of gravitational collapse.

Kind regards, Leonid.

Dear Rajat: To expand on Leonid's answer, cosmologists tend to think in terms of the "equation of state" when they think of matter. More specifically, they write w = p/ρ, where p is the pressure, ρ is the energy density of the substance in question, and therefore w is a dimensionless number (the units of dimension for energy density and pressure are the same: force over area is the same as energy over volume.)

For matter with no pressure, w = 0. This can include a dilute, nonrelativistic gas; it can be stars and planets (sure there is lots of pressure deep inside a star, but a swarm of stars behaves like a cloud of particles with no repulsive force between them, i.e., no pressure); it can be genuine inorganic dust (e.g., small chondrite particles); or it can even be "cold dark matter", also called "collisionless dark matter", which is a hypothetical form of dark matter with zero or near zero pressure.

Another good example is w = 1/3: this is the equation of state for an ultrarelativistic gas. Very early in the universe, it is believed to have been dominated by photons (i.e., most of the energy density of the universe was in the form of radiation), so this would have been the appropriate equation of state to use.

Yet another important example is w = −1. This is the equation of state that corresponds to the cosmological constant or dark energy. Yes, it means negative pressure. It also has the curious property that as the universe expands, the energy density of dark energy does not decrease. As the energy density of all other stuff goes down, ultimately dark energy prevails, and its presence accelerate the expansion due to its negative pressure.

Anyhow, the short answer to your question is that "dust" is just jargon for stuff with an equation of state of w = 0 (at least approximately.) This jargon is similar to the jargon used by astronomers who call every element in the periodic table other than H and He a "metal".

Dear V. T. Toth:

   You have provided a good answer to a good question.

I would like to discuss the some additional and important property of stiff mater EOS p=\rho. One asserts (for example Pawel O. Mazur and  Emil Mottola in gr-qc-0109035) that this EOS "the most extreme one allowed by causality". Why so it?

Dear L. D. Lantsman: It has to do with the speed of sound. The speed of sound in a perfect fluid with constant equation of state is given (in units where c = 1) as vs = √w. (It is a special case of the more general formula, vs2 = ∂p/∂ρ.) So if w > 1, we have vs > c, thus sound waves propagate faster than the speed of light, violating causality.