Traditionally the cosmological equation of state of cold matter (so-called dust) is simply: $$p = 0.$$ But, in Newtonian terms, each particle is gravitationally attracting every other particle. ...
In an article from the reference there are following words (page 2): "...pressure P is a Lorentz invariant... the result follows from standart properties of the relativistic stress-energy tensor...". ...
In the diagonal terms of the energy-momentum tensor, the flow of $x$-momentum in the $x$-direction is the $x$-pressure. Why the flow of momentum is pressure?