Cosmological constant as a fluid

[EDerkatch]

Hi everyone,

If anyone could point me in the right direction with this problem I'd really appreciate it.

"Show that the cosmological constant can be interpreted as a perfect fluid having an equation of state w=-1."

I have a rough idea of how to do the second part of the proof: if the cosmological constant can be interpreted as a perfect fluid then

ρ(dot)+3(a(dot)/a)(ρ+P)=0 (conservation equation)=>ρ+P=0 due to the continuity of a perfect fluid.

But how do I show that it can be interpreted as a perfect fluid?

 

[smallphi]

You have to take the Einstein equation with cosmological constant term included, move that term on the side of the energy momentum tensor and demonstrate the term looks exactly like energy momentum tensor of perfect fluid in its rest frame. Then you read off the energy and pressure of the fluid, in the rest frame, in terms of the cosmological constant and their ratio turns out to be -1. I won't say anything more than that.