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Correct me if I am wrong (it is in fact part of my question :) ) but from the little I know about the cosmological constant, growing existing evidence is still insufficient to tell whether $\Lambda$ is positive, zero or negative.

In case it is true, I would like to know whether there exist any explanations why the growing amount of data keeps failing to give a decisive answer. Seemingly what is known indicates that $\Lambda$, if nonzero, is very very small. Is it true? Is there a good reason for that?

Or, in case it has been already established, could anyone describe the consequences of the current knowledge of $\Lambda$?

DanielSank
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მამუკა ჯიბლაძე
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    The bound from cosmology is, if I remember correctly, something of the order $|\Lambda|<10^{-50} m^{-2}$. The error bars around zero are small, but nonzero nonetheless. So we cannot know yet if there is a positive or negative sign. – Clever Jan 12 '15 at 13:29
  • Don't we know that the expansion is accelerating http://en.wikipedia.org/wiki/Accelerating_universe (only possible with a positive constant). – Kevin Kostlan Jan 12 '15 at 18:40

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The big problem with finding the sign of the cosmological constant is that regardless of whether it is positive, negative, or zero, its magnitude seems to be very small. This means that while we have done a great job of pushing down our error bounds, they still contain both positive, negative, and zero values for the cosmological constant. As an aside, note that if the cosmological constant is truly zero, then no matter how carefully we measure it we will always have error bounds that contain both positive and negative values, and so we would have to find some other way to conclude that its value is zero.

A comment to the question above asks why the fact that the universe's expansion is accelerating doesn't prove that the cosmological constant has positive sign. The reason for this is simple: there are different reasons why the universe's expansion could be accelerating. If the accelerating expansion is due to a cosmological constant, then such a constant would have to be positive. This is the foundation of the $\Lambda CDM$ model of cosmology, but it isn't the only option. Dark energy does not have to take the form of a cosmological constant; it could be something else entirely. If this is the case, the fact that the expansion of the universe is accelerating has no bearing on the sign of the cosmological constant.

Because we know so little about the nature of dark energy, we can't make any clear-cut conclusions about whether or not it is simply a cosmological constant.

JotThisDown
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  • Thank you for the clear answer. What I still don't get however is this - is any theoretical mechanism known which would explain why it is so small? – მამუკა ჯიბლაძე Jan 12 '15 at 20:24
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    I'll try taking a stab at your last question. In an oversimplified manner I believe the cosmological constant is like the reciprocal of a time constant in the field equation. A very large time constant. That's what makes it small. The uncertainty in sign determines convergence towards some equilibrium or else unstable divergence. – docscience Jan 12 '15 at 20:34
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    @Jed Thomson So the fact that our universe is expanding, and at an accelerated rate either comes from the field equations parameters (which may be the cosmological constant itself) or else some force external to the model (field equations)? Any other possibility - other than the model structure being wrong in the first place? – docscience Jan 12 '15 at 21:15
  • @docscience Well it's always possible that the model is wrong in some way, but general relativity and Einstein's field equations have made enough correct predictions to warrant keeping them until we have evidence for something else. And within the framework of general relativity, the accelerating expansion of the universe could be due to a cosmological constant or to something else entirely (like some exotic form of matter that we have yet to discover). We really don't have an answer yet. – JotThisDown Jan 13 '15 at 00:57