The sign of the cosmological term

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    Cosmological Sign Term
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Discussion Overview

The discussion revolves around the sign of the cosmological term in the Einstein field equations, exploring its implications in different sign conventions and its relationship to dark energy. Participants examine the mathematical consistency of these conventions and their interpretations in cosmology.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that the cosmological term appears as -Λgik for the (+---) convention and +Λgik for the (-+++) convention.
  • Another participant expresses intuitive agreement with this observation, linking it to the Friedmann equation where Λ appears with a minus sign, suggesting a relationship between the two equations.
  • A reference to a Wikipedia article is made, indicating that sign conventions in general relativity are complex and that there are multiple classifications of these conventions.
  • A participant requests clarification on the specific section of the referenced work that discusses sign conventions.
  • Further discussion includes a participant's interest in dark energy and the implications of transposing the cosmological term to the right-hand side of the equation, reiterating the sign conventions.
  • One participant corrects another's terminology, clarifying that it is negative pressure being discussed, not negative momentum.
  • Questions arise regarding the relationship between pressure and momentum flux, with references made to definitions and relationships in fluid dynamics.

Areas of Agreement / Disagreement

Participants express varying interpretations of the sign conventions and their implications, indicating that multiple competing views remain without a clear consensus on the matter.

Contextual Notes

Participants acknowledge the complexity of sign conventions in general relativity and the potential for confusion, particularly in the context of dark energy and its representation in equations.

sweet springs
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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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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 = H∞2 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:
Ibix said:
Misner, Thorne and Wheeler classify eight different conventions
Could you tell which section?
 
Shyan said:
Could you tell which section?
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.
 
Thanks for your enlightenmental replies. I would likt to know more about dark energy, i.e. cosmological term transposed to right hand side, referring

sweet springs said:
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.

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.
 
sweet springs said:
The positive energy and the negative momentum are not usual.

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.
 
Is pressure the momentum flux? Force/area = Momentun density * velocity of fluid = momentum flux
 

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