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agingjb
2008-Oct-19, 03:44 PM
1) Is the "cosmological constant" necessarily a constant?

2) If not, could it vary locally?

(I'm going to guess that the answers are "yes" and "no".)

StupendousMan
2008-Oct-19, 03:48 PM
1) Is the "cosmological constant" necessarily a constant?


No. Many cosmologists predict that it might vary with time. Some scientific projects running now, or planned to run in the near future, will look for evidence that it might have a different value at different times.



2) If not, could it vary locally?


That particular sort of variation -- from place to place, rather than from time-to-time -- is one that I have not seen in the literature. But I'm an observer, not a theorist, so don't take my word for it.

Tim Thompson
2008-Oct-19, 05:12 PM
1) Is the "cosmological constant" necessarily a constant?
2) If not, could it vary locally?
(I'm going to guess that the answers are "yes" and "no".)

You are half right. No, the cosmological constant is not necessarily constant. But No, it could not vary locally. The only variation you can get in the cosmological constant is to make it time variable, as StupendousMan has already pointed out.

Most cosmologists do in fact think of the cosmological constant as being really constant. Once we allow for any variability, it is much easier to completely generalize the variability over both time & space. When we do that we do not put the variability in the cosmological constant at all, but rather assume the presence of a variable scaler (i.e. not a vector) field that is included in the stress-energy tensor in Einstein's equations. And of course you could have both a cosmological constant and a variable scalar field. Quintessence Cosmology is one of the ideas which is built on the scalar field idea. "Dark Energy" is a placeholder concept that is usually associated with a cosmological constant (which could be variable).

The observational data thus far appears to favor the idea of a cosmological constant that is in fact constant, and no variable scalar field (i.e., Kowalski, et al., 2008 (http://adsabs.harvard.edu/abs/2008arXiv0804.4142K)) but the constraints are not strong.

Ken G
2008-Oct-19, 05:18 PM
The cosmological constant, meaning that particular term in the gravity equation, could vary in any way. We haven't the vaguest idea what this thing is. All we can say is that we are going to assume it is constant in both space and time unless we have to do something different, and we're going to justify that assumption based on both its simplicity, and the idea that "vacuum is vacuum". If we are forced to posit variation, it does seem a lot more plausible that it might vary with time than with location, but what do our "plausibility guesses" really mean? It's true that if it had some spatial variation for no apparent reason, we could no longer use the "cosmological principle", which would be a huge change in our thinking and would really be extremely surprising. But so what? Or, if we say it depends on the local mass distribution, then it's part of the dynamics and perhaps has a very different flavor from what we would call the "cosmological constant", but that's kind of a separate question-- the question of what we even mean by a cosmological constant.

Eroica
2008-Oct-20, 07:46 AM
One way of looking at inflation is to say that during inflation the value of the cosmological "constant" was much much greater than it is now so that the inflating universe was dominated by it (a cosmological model known as the de Sitter model (http://en.wikipedia.org/wiki/De_Sitter_cosmology)).

agingjb
2008-Oct-20, 08:13 AM
Thanks everyone.

I don't pretend to have a clue about this, but a "lay" observation: if the "constant" could vary over time, then how would whatever it really is maintain simultaneity at a distance?

Ken G
2008-Oct-20, 02:12 PM
I don't pretend to have a clue about this, but a "lay" observation: if the "constant" could vary over time, then how would whatever it really is maintain simultaneity at a distance?

That's a good question. The best answer might be, it wouldn't. However, the basic point of "inflation" is to make the whole universe we see (which is causally unconnected, as you say) come from a region that is causally connected. Put differently, the question you are raising about the cosmological constant is already there for the temperature of the CMB-- why is that temperature the same everywhere, as though the entire universe we see is causally connected even though it isn't?

Or another way to say that, let's say the cosmological constant varied over time over a caually unconnected region. Like you say, that should give rise to spatial variations also. But if you have an inflationary period, then all those different regions inflate at different rates, but by a huge amount. Each different inflation rate generates a post-inflationary universe with drastically different properties. If we apply a "landscape" kind of idea (the full "landscape also plays with the other fundamental constants, not just the cosmological constant), then most of those "mini-universes" would not be conducive to intelligent life, so we end up in the mini-universe with the appropriate cosmological constant to sustain intelligent life (that's the strong anthropic principle).

Then the weak anthropic principle says that, in this mini-universe, intelligent life should come along at about the time when the cosmological constant is just starting to become important to the post-inflationary expansion. So one can tell a cogent story, where no causality effects are violated, but it's not obvious if this story is testable science.