Cosmological Constant Term in Einstein Equations

[kent davidge]

One side of the Einstein Equations with a cosmological constant is $R_{\mu \nu} - (1/2) Rg_{\mu \nu} + \Lambda g_{\mu \nu}$.

Question is, why the cosmological constant term appears with a plus sign and without a factor of 1/2 in front of it?

I guess it may be because $\Lambda$ is (in principle) just any constant, so both the minus sign and the 1/2 factor can be absorbed into it?

 

[PeterDonis]

Question is, why the cosmological constant term appears with a plus sign and without a factor of 1/2 in front of it?

The sign is just a convention, since $\Lambda$ can have either sign.

Why would you expect a factor of 1/2 in front?

 

[haushofer]

It depends on how you write down Lambda in the action.