# The sign of the cosmological term

1. Jun 27, 2015

### sweet springs

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 $-\Lambda g_{ik}$ for (+---) convetion or $+\Lambda g_{ik}$ for (-+++) convetion. Right?
Best

2. Jun 28, 2015

### marcus

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
3. Jun 28, 2015

### Ibix

4. Jun 28, 2015

### ShayanJ

Could you tell which section?

5. Jun 28, 2015

### Ibix

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.

6. Jun 28, 2015

### sweet springs

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. $\Lambda g_{ik}$ for (+---) convetion or $-\Lambda g_{ik}$ 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.

7. Jun 28, 2015

### bcrowell

Staff Emeritus
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.

8. Jul 2, 2015

### sweet springs

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

9. Jul 2, 2015

### bcrowell

Staff Emeritus