I am reading a book in which it is claimed that one of the universal constants that has to have a certain value is the cosmological constant and that it has to be correct to 120 decimal places. Is this true? That it exists was discovered only about 15 years ago (yes Einstein used it, but famously abandoned it) and I cannot imagine how it could accurately measured to even one decimal place, since the evidence is based on very distant supernovas.
Could he have meant something like the fine structure constant?
Definitely wrong. I think they were either confused by the measured cosmological constant is 120 orders of maginitude smaller than a naive prediction of the cosmological constant from quantum field theory (the so-called worst prediction in physics) or the fact that written in natural units the cosmological constant is about 10[sup]-122[/sup]. It’s value is only known to about 1 sig figs.
Was this discussion with regard to the ‘fine tuning’ problem? Because IIRC, there’s only a relatively small region in parameter space which yields a universe capable of giving rise to sentient observers; if it’s too big, the necessary structures never form, and if it’s too negative, the universe re-collapses before enough time has passed. Weinberg produced an argument based on these considerations limiting its value to within about two orders of magnitude from what is actually observed, before it was discovered that it actually has a nonzero value. Perhaps what you read was a garbled account of this?
Yes it was in connection with the fine tuning problem. It began by mentioning that if gravity was too strong stars would collapse and if too weak would never form and a couple other constants that would preclude life, all of which I understand, then I came on the passage from my OP. Which, for reasons I explained, didn’t seem credible. The book (called “The Outer Limits of Reason” by Noson Yanofsky) is otherwise very reliable, insofar as I could judge. I will write the author and ask him what he was thinking. But I wanted to make sure I was right. Is the cosmological constant even important to the existence of life?
Well, as I said, the argument is that if it’s too large, the formation of structures like we observe, such as galaxies, or even solar systems, in the universe never takes place, while if it’s negative (and has a too great absolute value), it collapses too early. Of course, to abstract from these constraints to an impossibility of life forming depends on some assumptions, and depending on the strength of these assumptions, you’ll get different predictions; it’s probably quite safe to say that if the cosmological constant is big enough to rip apart molecules or atoms, then you wouldn’t get the necessary basic stuff for complex, sentient organisms, and if it lasted only a few million years, then there just wouldn’t be enough time. But how far you need to relax this in order to get some complexity of the right sort—how similar a universe must be to ours in order to give rise to observers that aren’t necessarily similar to us at all—is probably anyone’s guess.
Ah yes, but I meant to say that if it were 0, I assume that would have no impact on life as we know it. I realize that if were 120 orders of magnitude larger, it would certainly prevent the formation of stars, galaxies, etc. If it were negative could we distinguish from a stronger force of gravity (which we already knew would have detrimental to life as we know it).
I thought Half Man Half Wit already answered this, so I’m not sure of what this question is. As long as the cosmological constant allows for a stable, long-lived universe then a range of values should allow the formation of life. But since we have no idea what constraints the universe might have for life other than what we know on earth, we can’t put any additional limits on that range.
It is currently calculated as 2.036 × 10[sup]-35[/sup]s[sup]-2[/sup], which may not be 0 but is closer than we can possibly ever physically measure.
If I’m misreading your question, sorry. Could you rephrase it?
Nitpick: That’s not closer to zero than we can possibly ever physically measure, since that number does in fact come from measurements. You just need a really, really big laboratory to measure it.
None that I could think of, no. But the argument by Weinberg I mentioned earlier, which later was refined by Vilenkin, favours a small, but positive CC—I think Vilenkin got it to within a factor three or so. The argument is based on anthropic reasoning, and relies on the existence of many universes beyond our own, to establish that the observed value of the CC should be close to the maximum that allows for galaxy formation. Personally, while it’s interesting that they got the value so close during a time everybody believed the CC to be zero, I must admit to being a little bit uncomfortable with these kinds of arguments—there seems to be some kind of circularity inherent in explaining the universe we’re seeing from the fact that we’re seeing this universe.
I have a cosmological constant question which I hope is not a major hijack.
Is the current existence of an expansionary force (the cosmological constant) at all related to the prior era of inflation? By this I do not mean a relic of prior inflation, but instaed a different, far weaker inflation, caused by a different (presumably far weaker)scalar field.
If so, what would be the consequences of the ‘phase transition’ when this episode of inflation ends? I’ve heard the prior ‘phase transition’ would have been quite dramatic, with release of much energy.
The best guess anyone has is that, since current cosmic expansion produces a result qualitatively like that of inflation, it might be due to an underlying process similar to that of inflation. So the answer to your question is a definite “maybe”. But there’s a vast amount we don’t know about the mechanism behind the acceleration of the Universe, and nobody would be particularly surprised to discover that everything we think we know about it is wrong.
If the Universe does go through another such phase transition, it would be the end of the world as we know it, and we have no reason to believe that anything we could make or do would survive the process in any meaningful sense.
Thankfully, though, it won’t necessarily happen: The Universe during inflation was in what’s called a false vacuum state: It was in an energy state that was a local minimum, but not actually in the true vacuum global minimum energy state, so it was possible for it to get disturbed out of the false vacuum it was in down to a lower state (one in which inflation was no longer possible). Now, it’s possible that the state it transitioned to (our state) is also a false vacuum, and will eventually be disturbed to a lower state yet… But it’s also possible that we really are in the ground state, the true vacuum, right now. The fact that our current state includes a phenomenon we didn’t expect before is not in any way an indication that it’s a false vacuum.
As I understand it, that value was calculated by feeding several numbers in an equation. None of the individual measurements were to 35 significant figures. That’s what it looks like in Value of the Cosmological Constant: Theory versus Experiment [pdf]. We can’t directly measure anything to 35 decimal places and we never will be able to. The 10[sup]-52[/sup]m[sup]-2[/sup] equivalent is even worse.
I may be misunderstanding something obvious, to be sure. But since 35 decimal places for pi will give you the diameter of the universe to the width of a proton, or whatever that piece of trivia is, I don’t think I’m going out on a limb by saying we can’t measure anything that well.
A figure of 10[sup]-52[/sup] m[sup]-2[/sup] does not have 52 significant digits, or 35 significant digits. It might have one significant digit, and probably not even that. The number of significant digits a measurement has does not depend on what units you’re using to measure it (well, it might change by at most 1, since digits are discrete, but not beyond that).
The precise value of 2.036*10[sup]-35[/sup]s[sup]-2[/sup] is indeed a calculation, based on a speculative model of cosmology the details of which I’m not familiar with, and which seems not to have generated much of an impact (the paper has 12 citations since 2001, many of which are due to its authors); it’s not a standardly accepted value, to my knowledge. The currently accepted experimental value of the CC is just 10[sup]-35[/sup]s[sup]-2[/sup], which is correct to within experimental accuracy, i.e. one significant digit (a value of zero, for instance, is ruled out to near certainty); likewise for the equivalent 10[sup]-52[/sup]m[sup]-2[/sup], or even 10[sup]-122[/sup] in natural units. Perhaps a better way to express the value of the CC is in terms of a ratio to the universe’s critical density (which, in universes without a CC, denotes the boundary between universal contraction and expansion), where it is currently about 0.69 +/- 0.1. That way, you don’t have any of the counterintuitive features of numbers with small absolute values.
If there’s any reason why life can’t exist with the cosmological constant being either postive or negative and having a value several orders larger/bigger than it’s current absolute value they would be fairly subtle. For example a cosmological constant about 2 orders bigger than it currently is would reduce the scale over which the ‘repulsion’ of dark energy overcame the attraction of gravity by about one order, which isn’t much considering how big that scale already is and is comfortably enough to allow stars and galaxies to form.
The cosmological constant isn’t a term that simply makes gravity stronger or weaker either. For example if this were the case the Einstein static Universe would be stable.