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The sign of the cosmological term

  1. Jun 27, 2015 #1
    I want to know the sign of the cosmological term. It seems that in the left hand side of the Einsetein equation the cosmological term is [itex]-\Lambda g_{ik}[/itex] for (+---) convetion or [itex]+\Lambda g_{ik}[/itex] for (-+++) convetion. Right?
    Best
     
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  3. Jun 28, 2015 #2

    marcus

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    That makes intuitive sense to me. I hope someone shows up who can confirm this more authoritatively. The reason it makes sense to me as a non-expert is that Λ shows up with a minus sign in the Friedmann equation in cosmology. The Friedmann is supposed to be derived from the "0 0" component of the GR equation , that is from the "t t" components term by term. And the Friedmann equation looks like this:
    H2 - Λc2/3 = [constant] ρ

    where H is a fractional growth rate with dimension Time-1 so H2 has dimension Time-2, and rho is the density.
    Λ has dimension Length-2 so Λc2 also has dimension Time-2, so that is consistent.
    And Λc2/3 = H2 the square of the longterm Hubble expansion rate to which H(t) is converging.

    So I think of Λ as appearing with a + sign on the left side of the GR equation, in the (-+++) convention and therefore appearing with a - sign on the left side of the Friedmann.
     
    Last edited: Jun 28, 2015
  4. Jun 28, 2015 #3

    Ibix

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  5. Jun 28, 2015 #4

    ShayanJ

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    Could you tell which section?
     
  6. Jun 28, 2015 #5

    Ibix

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    The very first page (it's red in my copy) is a table of sign convention by author. There are eight possibilities in their classification scheme; I haven't actually checked that they have an example of every one in use.

    Edit: The above isn't directly related to the OP's question - it was more in the vein of a general caution.
     
  7. Jun 28, 2015 #6
    Thanks for your enlightenmental replies. I would likt to know more about dark energy, i.e. cosmological term transposed to right hand side, reffering

    i.e. [itex]\Lambda g_{ik}[/itex] for (+---) convetion or [itex]-\Lambda g_{ik}[/itex] for (-+++) convetion. The positive energy and the negative momentum are not usual.
    I would like get some interpretation or explanation of this combination. If you know something good please let me share it.
    Best.
     
  8. Jun 28, 2015 #7

    bcrowell

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    It's negative pressure, not negative momentum. The momentum three-vector is a vector, so it doesn't make sense to talk about whether it's positive or negative.
     
  9. Jul 2, 2015 #8
    Is pressure the momentum flux? Force/area = Momentun density * velocity of fluid = momentum flux
     
  10. Jul 2, 2015 #9

    bcrowell

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