# Cosmology constant as a negative pressure?

It seems a positive cosmology constant behaves like a negative pressure. However, the positive cosmology constant cause a expanding universe. So I am puzzling about this:

A negative pressure cause a expanding universe?

To me, it is easy to imagine the positive pressure cause expanding just like gas. Could you give me a explanation about this?

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## 1 Answer

It does seem odd, but this is because in GR the Einstein tensor is proportional to the stress-energy tensor not just the mass. This is (commonly represented as) a 4x4 matrix and the dominant term is usually the energy density, $T_{00}$. However the other diagonal components $T_{11}$, $T_{22}$ and $T_{33}$ are the pressure. A positive pressure behaves like a mass and causes an attraction. Luboš Motl went into some detail on this in his answer to Why does pressure act as a source for the gravitational field?. A negative pressure has the opposite effect i.e. it causes a repulsion.

I've rather glossed over why pressure has a similar effect to energy density, because this isn't easy to explain in simple terms. John Baez had a go here, though I'm not sure I find this terribly convincing.

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Hi John, thank you for answering. – Yingfei Gu Nov 6 '12 at 8:38
Hi John, thank you for answering. It is good point to understand pressure as some kind of mass, or equivalently speaking the energy density. But I am still wondering "Does the analog of gas make sense here?" I mean the first picture in my mind when I see “negative pressure” is a shrinking bubble. I don't know if the pressure here means some real force in the universe. – Yingfei Gu Nov 6 '12 at 8:49
@YingfeiGu It's not an 'analog'. It IS pressure causing attraction/repulsion. But in most circumstances the effects of pressure are completely overshadowed so its negligible. In gases, even gravitation is (mostly) negligible, needless to say pressure! – namehere Dec 6 '12 at 10:22