Cosmological constant as a perfect 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?

 

[Poop-Loops]

My guess is if you can show that everything works the same if you interpret it as a perfect fluid and do your magic (whatever you just did), then you just showed that it can be interpreted that way.

What I mean is, you make the guess that it can, do some math, and if everything works out the same, then your assumption is valid.

 

[Dick]

If w=(-1) for a perfect fluid then rho+p=0. So by the conservation equation rho(dot)=0. Hence it's a constant. A 'cosmological constant'. Perhaps I don't understand the question?