(adsbygoogle = window.adsbygoogle || []).push({}); <<Mentor note: Edited for readability.>>

<<Follow-up: futher edited to fix LaTeX tags>>

Context: FRW Metric /universe, perfect comological fluid , dark/vacuum energy

So the equation of state ## w \rho=p, w=-1, \rho=-p##

so this clealy implies either ##p## or ##\rho## is negative.

Am I correct in thinking which it is, depends on the cosmological constant?

So ##cosmo constant >0, \rho>0, p<0##

##cosmo constant <0, \rho <0, p>0?##

Now I look at a Friedmann equation given by: ##\Omega -1 = \frac{k}{H^2a^2} ##, where ## \Omega = \frac{\rho}{\rho_{c}} ##, ##H=\frac{\dot{a^{2}}}{a^{2}} ##

and solving for ##a## as a function of ##t## for ##cosmo constant >0##, my book says that in this case ##\Omega <0 ## ( which I understand if my above reasoning is correct) and so from the Friedmann equation this is only possible if ##k=-1 ##. So this is fine, I agree , but the denominator needs to be greater than zero.

Anyway, it than solves for ## cosmo constant >0 ##, and says all ## k=-1,0,1 ## are fine. This is my QUESTION. I dont understand how ##k=-1## can be okay for both ##cosmo constant >0, <0 ## which in turn say different things above which of ## \rho ## and ##p## are negative and positive.

Thanks very much for your help.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# FRW. Dark energy, negative pressure or density?

**Physics Forums | Science Articles, Homework Help, Discussion**