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FRW. Dark energy, negative pressure or density?

  1. Mar 3, 2015 #1
    <<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.
     
    Last edited by a moderator: Mar 3, 2015
  2. jcsd
  3. Mar 3, 2015 #2

    Matterwave

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    You have to fix those Latex tags or else this is pretty unreadable...

    I see a note by a mentor saying it's been edited for readability, but this still looks pretty unreadable to me.
     
  4. Mar 3, 2015 #3

    PeterDonis

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    2016 Award

    Staff: Mentor

    Yes.

    I think you mean for ##cosmo constant < 0##, correct? That's the case for which ##\rho < 0##, which makes ##\Omega < 0##.

    ##k## describes the spatial curvature; it doesn't describe either the density or the pressure associated with the cosmological constant. All this is saying is that "open" spatial slices (i.e., negative spatial curvature) are compatible with both a positive and negative cosmological constant.
     
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