Sunday, December 08, 2013

Negative Pressure

One of the less intuitive notions in trying to understand dark energy is the idea that negative pressure, or tension, should increase the expansion rate of the universe. Sean Carroll and Lubos Motl have each taken recent (battling) cracks at explaining this. Lumo, at least, takes exception to Sean's explanation.

I won't comment on the debate, but I thought I might pass on this idea (adapted from Wikipedia) on why a cosmological constant implies negative pressure.

Consider a box, or maybe a piston. If ordinary positive pressure exists in the cylinder, and expands the volume by dV, the pressure does work pdV and the energy in the box decreases (by the same amount, in an adiabatic process). Suppose though, that space is filled with a something (dark energy) of constant energy density rho. Now a change in volume of the cylinder will increase the amount of dark energy by rho*dV. If we go back to our W = p*dV we note that the cylinder did work - rho*dV in expanding so that p = -rho.

QED