Is the Cosmological Constant Truly Constant?

[jfy4]

Hi,

I am wondering if the cosmological constant is a constant in the sense that it can only have one value, ie some constant element of the reals, or if it can be a scalar function too dependent on the coordinate variables, eg \Lambda(r,t).

Thanks in advance,

 

[atyy]

Usually it's constant to maintain that the divergence of the stress-energy tensor is zero.

I think there are ways of adding it not to the field equations, but to the action, and varying with respect to it, to also maintain energy conservation. http://arxiv.org/abs/gr-qc/0505128

 

[jfy4]

Usually it's constant to maintain that the divergence of the stress-energy tensor is zero.

I think there are ways of adding it not to the field equations, but to the action, and varying with respect to it, to also maintain energy conservation. http://arxiv.org/abs/gr-qc/0505128

That makes sense. If I may, would the satisfaction of
\nabla_{\beta}\left( T^{\alpha\beta}-g^{\alpha\beta}\Lambda\right)=0
justify the inclusion of a cosmological constant that was a scalar function?

 

[atyy]

That makes sense. If I may, would the satisfaction of
\nabla_{\beta}\left( T^{\alpha\beta}-g^{\alpha\beta}\Lambda\right)=0
justify the inclusion of a cosmological constant that was a scalar function?

Do you mean something like the potential of a scalar field forming part of the stress-energy tensor of matter (http://ned.ipac.caltech.edu/level5/Carroll2/Carroll1_3.html" )?

 

[jfy4]

Do you mean something like the potential of a scalar field forming part of the stress-energy tensor of matter (http://ned.ipac.caltech.edu/level5/Carroll2/Carroll1_3.html" )?

Thanks for your help,

I think this answers my question.

Classically, then, the effective cosmological constant is the sum of a bare term \Lambda_0 and the potential energy V(\phi), where the latter may change with time as the universe passes through different phases.

This sounds like it is ok to include a cosmological constant of the form
\Lambda(x_{\alpha})=\Lambda_0+V\,[\phi(x_{\alpha})]
that consists of an initial cosmological constant, \Lambda_0, summed with a scalar function V. Have I interpreted this correctly?

 

[haushofer]

Hi,

I am wondering if the cosmological constant is a constant in the sense that it can only have one value, ie some constant element of the reals, or if it can be a scalar function too dependent on the coordinate variables, eg \Lambda(r,t).

Thanks in advance,

The LHS of the Einstein equation should be divergenceless, because the right hand side is (energy momentum conservation). This brings one to the addition of a term

<br /> \Lambda g^{\mu\nu} \ \ \rightarrow \nabla_{\mu}(\Lambda g^{\mu\nu}) = \nabla^{\nu}\Lambda = 0<br />

So,

<br /> \partial_{\mu} \Lambda = 0<br />

Hence, lambda must be a constant.