# Cosmological Constant & Fine Tuning for Life

Hi, I have some confusion about the cosmological constant (CC). From what I have read it is to do with the energy density throughout the entire universe which is thought to drive the expansion of the universe. If the CC were any smaller then matter would not have been able to form and since the number is so small it means that life is extremely finely tuned. I have watched a few lectures online from decent professors (like Susskind) but different people quote the CC in different units. Susskind quotes it in dimensionless units which give a number of 10 to the power of -122. Other professors quote it as 10 to the power of -29 in units of grams per centimeter cubed. Both argue how fined tuned life because of how small the number is but how fined tuned is it? These two numbers differ by 93 orders of magnitude. Can you really just change the units from grams/cm^3 to dimensionless units and argue that life is fined tuned to an order of -122? That's seems ridiculous to me.

mathman
You have hit upon one of the major open questions in current cosmology. Until about fifteen years ago most worker in cosmology thought it was 0. However the discovery at that time (by two groups working independently) that the universe was speeding up led to the need for a non-zero value. Why that particular value has led to a lot of speculation, such as multi-verse.

1 person
You have hit upon one of the major open questions in current cosmology. Until about fifteen years ago most worker in cosmology thought it was 0. However the discovery at that time (by two groups working independently) that the universe was speeding up led to the need for a non-zero value. Why that particular value has led to a lot of speculation, such as multi-verse.
Thanks for the reply. Why is there two different values quoted? I mean I know their different units which gives the different values but which one is more meaningful?

Ken G
Gold Member
There are always two ways to express any physical quantity, either in dimensionless units or in some fixed dimensions. You can make an argument that the quantity is "small" either way, but the argument is different. If you use the dimensionless version, it means you are scaling all quantities to combinations of the physical constants in your theories, c, G, and h. These quantities are fundamental to the theories being used, they do not reflect any measurements that humans can do, or anything that reflects the human sphere, they are simply what seem "natural" to the universe itself. So when you get 10-122 in those units, it means the universe has picked an extremely small value for that parameter, when the constants c, G, and h are regarded as the fundamentally natural scales (since they are fundamental to the theories).

If you use the dimensional version, it generally means that all quantities are being compared to observations in human experience, because such observations are generally the reasons we have the units we do. So when you get a "small" quantity in those units, it simply means the quantity is strangely small compared to the things we are used to experiencing. This turns out to be not nearly as small as the "natural" result that doesn't care about the scales of human experience, which tells you that the scale of human experience is already strangely "large." Since our scales are dwarfed by the whole universe, we also see that the universe is amazingly "large" compared to its "natural" scale.

So these are the big puzzles, all interrelated: why is the universe so incredibly large, why are humans pretty darn large, and why is the scale of dark energy so incredibly small? The universe is very "non-generic", but you can regard that property in two ways: it is non-generic in relation to the physical constants (the Susskind approach, who tends to be rationalistic so of course he thinks in terms of the constants as being fundamental), and it is also non-generic in relation to the scales of human experience (the "other professors" approach, which likely means those professors tend to be more empiricist, so care about the scales of human experience). That it is less non-generic in the latter case is a reflection of the fact that human experience itself appears to be highly non-generic in relation to the physical constants. Neither is wrong, it's just the perspective you take.

1 person
Chalnoth
If the CC were any smaller then matter would not have been able to form and since the number is so small it means that life is extremely finely tuned.
This statement isn't quite right. If the cosmological constant were closer to zero than it is, everything would be just fine. However, if it were significantly larger than its present value, it would cause the accelerated expansion of the universe to happen so soon that normal matter would never have any time to get together, and no stars or galaxies would form. If I recall, this would have happened if the cosmological constant were somewhere around 10-100 times its present value (or more).

Alternatively, if the cosmological constant had been negative and about 10-100 times its present value or more, then it would cause the universe to collapse back in on itself before any life would have a chance to form.

1 person
Ken G
Gold Member
isn't it more finely tuned than that? Weinberg famously predicted its value, and as I recall he felt he had both a lower and an upper bound to his prediction. This is often regarded as the first (only?) success of multiverse theory, although it could also be said that a value of the CC that is consistent with us being here is not actually evidence for the value of any theory other than GR with a CC.

1 person
Chalnoth
isn't it more finely tuned than that? Weinberg famously predicted its value, and as I recall he felt he had both a lower and an upper bound to his prediction. This is often regarded as the first (only?) success of multiverse theory, although it could also be said that a value of the CC that is consistent with us being here is not actually evidence for the value of any theory other than GR with a CC.
One hundred times its current value would still be ##10^{-120}##. That is still very finely-tuned.

Chronos
Gold Member
It is obviously illogical to argue any version of cosmology that forbids observers such as ourselves. On that basis, I find it similarly illogical to assume we are alone in the universe.

Ken G
Gold Member
One hundred times its current value would still be ##10^{-120}##. That is still very finely-tuned.
But when Weinberg predicted the value of the CC, he predicted it would not be zero either. So he did argue we needed a CC in order to be here, and that was later verified. This may mean he well understood all the ramifications of accelerated expansion, though it doesn't mean we live in a multiverse. Still, for some reason he did see acceleration as a requirement for us to be here.

Ken G
Gold Member
It is obviously illogical to argue any version of cosmology that forbids observers such as ourselves. On that basis, I find it similarly illogical to assume we are alone in the universe.
Certainly it is a big universe, so unless there are some drastically small probabilities we really don't understand, we should not be alone. But it's always possible that it is vastly unlikely for some reason we are missing. For example, in multiverse thinking, the most common number of intelligences in a member of the multiverse set that contains any intelligences is probably 1, since the vast majority would have 0, and then 1 should be the next most common. But if we sample over intelligences, rather than over universes, what becomes the most likely number of other intelligences in the same universe? That depends on the distribution chosen for the multiverses, but I wouldn't be surprised if you'd likely get a vast number as that answer. Could that kind of thinking be used to estimate the number of intelligences? I don't see how, not without knowing something about the distribution-- that always seems to be the problem with multiverse thinking.

isn't it more finely tuned than that? Weinberg famously predicted its value, and as I recall he felt he had both a lower and an upper bound to his prediction. This is often regarded as the first (only?) success of multiverse theory, although it could also be said that a value of the CC that is consistent with us being here is not actually evidence for the value of any theory other than GR with a CC.
He did indeed have a lower bound. The major difference to other predictions was that he was predicting a non zero value, before experimental evidence emerged for it. If I recall correctly his prediction was within and order of magnitude and later predictions following his method got it to within a factor of about 3. This is pretty remarkable for such a small number.

It's worth noting that multiverse is a term that has been used to describe something as simple a large whole universe, of which our observable universe represents a small fraction. This much isn't controversial. I don't think any serious cosmologist is arguing that our observable universe is the whole universe anymore. However, if this were to provide an explanation for the observed value of the cosmological constant then we would require it to vary, with some regions of space expanding faster than others and others having collapsed. This gives rise to a complex shape to the universe and the posibility of pockets of space-time becoming isolated from each other and a much more exotic notion of a multiverse.

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Ken G
Gold Member
True, and it's even more problematic than that-- to "explain" fine tuning with a multiverse, you must let the members of the multiverse set have not only different Hubble constants, but even different h, c, and G. So if you do that with one single universe with some kind of eternal inflation going on, you still have to find a way to make the parameters different in each pocket. Whether you call that one universe or many doesn't really matter-- what matters is whether or not you will regard such a proposition as science or not, if you cannot actually do an experiment that obtains different h, c, or G.

Chalnoth
But when Weinberg predicted the value of the CC, he predicted it would not be zero either. So he did argue we needed a CC in order to be here, and that was later verified. This may mean he well understood all the ramifications of accelerated expansion, though it doesn't mean we live in a multiverse. Still, for some reason he did see acceleration as a requirement for us to be here.
I think you're misunderstanding slightly. Structure formation essentially requires ##-10^{-120} < \Lambda < 10^{-120}##. The non-zero prediction was simply a statement that a cosmological constant of zero would be infinitely finely-tuned, and therefore unlikely. It could easily be closer to zero, it's just not likely because there is less parameter space closer to zero.

Ken G
Gold Member
OK, that does make sense, Weinberg may have expected a CC simply because it seemed more likely to have the largest one consistent with intelligent life than none at all. If so, it's not very convincing that he didn't just get lucky-- unless we wish to globally accept a provision that says any parameter I can invent that could be zero should instead take on its largest possible value that would be consistent with the presence of intelligent life! Still, the point is, he felt that he could make a prediction of a physical quantity that had not been verified, simply on anthropic grounds. He interpreted that success as evidence in favor of a multiverse, although no doubt other explanations are possible as well-- including any explanation that sees a nonzero CC to be more likely than a zero one, and noting that the CC must be consistent with our presence.

Chronos
Gold Member
Weinberg's CC prediction is pretty unremarkable, IMO. You could also predict the oxygen content of earth's atmosphere must be around 20% based on the weak anthropic principle. Would anyone find the success of that prediction as compelling evidence for a multiverse?

Ken G
Gold Member
The problem is, they wouldn't use that as evidence of a multiverse, they'd use it as evidence of the existence of other planets. Let's say the Earth was the only planet in our solar system, so no other planets had ever been detected, and people were wondering if other stars had planets. They'd say if the Earth was the only planet, how come it has the right amount of oxygen for us to be here? So there must be other planets, with other amounts of oxygen.

Now I agree that this is not an ironclad argument. It would seem strange that our Sun found a way to have a planet, and the 1011 other stars in our galaxy didn't. So we'd have to say the Earth is surrounded by a fog such that we never even see any other stars-- can we still argue that other stars must exist, because otherwise why would the Earth have 20% oxygen? Or would we argue that our Sun must have a vast number of planets orbiting it, and we never even thought of other stars? Or should we say the oxygen on Earth went through many stages, and we are in the stage that works for us? That's the problem, without observations of other universes, the whole concept seems very weakly constrained, and some might be right and others wrong, with little chance of knowing which is which.

The problem is, they wouldn't use that as evidence of a multiverse, they'd use it as evidence of the existence of other planets. Let's say the Earth was the only planet in our solar system, so no other planets had ever been detected, and people were wondering if other stars had planets. They'd say if the Earth was the only planet, how come it has the right amount of oxygen for us to be here? So there must be other planets, with other amounts of oxygen.

Now I agree that this is not an ironclad argument. It would seem strange that our Sun found a way to have a planet, and the 1011 other stars in our galaxy didn't. So we'd have to say the Earth is surrounded by a fog such that we never even see any other stars-- can we still argue that other stars must exist, because otherwise why would the Earth have 20% oxygen? Or would we argue that our Sun must have a vast number of planets orbiting it, and we never even thought of other stars? Or should we say the oxygen on Earth went through many stages, and we are in the stage that works for us? That's the problem, without observations of other universes, the whole concept seems very weakly constrained, and some might be right and others wrong, with little chance of knowing which is which.
There's also a subtle difference in that it's reasonable to presume that different atmospheric oxygen ratios could support intelligent life. If we put all the properties of the earth together it does seem rare. For example, temperature, not being tidally locked, abundance of the elements, the role of the core and moon, position in the galaxy, all seem important to the probability of supporting complex life. It's hard to deny that the earth is fine tuned for life in many different ways.

The weak anthropic principle in conjuction with the multiverse hypothesis just really suggests that there may be no way for us to experimentally verify any postulate about the natural constants. If this turns out to be broadly accepted then we're left with judging indistinguishable physical hypotheses based upon aesthetics rather than predictive capacity. The question then becomes are we just doing maths rather than physics. It's interesting to note that string theory has ended up in a very sinilar situation.

Chalnoth
Weinberg's CC prediction is pretty unremarkable, IMO. You could also predict the oxygen content of earth's atmosphere must be around 20% based on the weak anthropic principle. Would anyone find the success of that prediction as compelling evidence for a multiverse?
No, you couldn't. It's entirely conceivable that different chemistries could work just fine.

It's not conceivable that life can form if no compact objects form.

Ken G
Gold Member
If this turns out to be broadly accepted then we're left with judging indistinguishable physical hypotheses based upon aesthetics rather than predictive capacity.
And I hope we can perish the thought that science would ever be relegated to that, it would make it one of those other things that is not science and so relies on aesthetics rather than predictive power. We do have aesthetics in science, like Occam's razor, but we do not count that as evidence in the truth of a theory (if we may allow ourselves the pedagogical luxury of imagining that theories can be true). We must find predictive power in a theory or the theory is not science. So if we find we derive predictive power from a theory that also says we cannot understand why the constants are what they are, then so be it, but show me that predictive power before you show me the aesthetics. It must make a "risky prediction" in the Popper sense-- it must be a prediction that I would be inclined to doubt if I did not ascribe to the theory that produces it.
The question then becomes are we just doing maths rather than physics. It's interesting to note that string theory has ended up in a very sinilar situation.
Yes, this is a kind of crisis in modern physics, we are in some danger of coming full circle and returning to the mode of science used by the ancient Greeks, which was really more like philosophy before philosophy created science to carry out this particular task. The desire to feel we know sometimes trumps the requirement to demonstrate that we know.

Chronos
Gold Member
I think that fine tuning arguments have the tail wagging the dog. Earth is not fine tuned for life, life is fined tuned for earth. Similarly, this universe is not fine tuned for life, life is fine tuned for this universe. It is almost certain life could exist under a vast array of other combinations of chemistry, physics and conditions not necessarily similar to our own. But, that life would be finely tuned for those conditions and intelligent observers there would surely marvel, and probably philosophize about why/how their world/universe was fine tuned for their version of life.

Chalnoth
I think that fine tuning arguments have the tail wagging the dog. Earth is not fine tuned for life, life is fined tuned for earth. Similarly, this universe is not fine tuned for life, life is fine tuned for this universe. It is almost certain life could exist under a vast array of other combinations of chemistry, physics and conditions not necessarily similar to our own. But, that life would be finely tuned for those conditions and intelligent observers there would surely marvel, and probably philosophize about why/how their world/universe was fine tuned for their version of life.
Depends upon what you're talking about. There's not going to be any way for life to form if there aren't any compact objects.

I think that fine tuning arguments have the tail wagging the dog. Earth is not fine tuned for life, life is fined tuned for earth. Similarly, this universe is not fine tuned for life, life is fine tuned for this universe. It is almost certain life could exist under a vast array of other combinations of chemistry, physics and conditions not necessarily similar to our own. But, that life would be finely tuned for those conditions and intelligent observers there would surely marvel, and probably philosophize about why/how their world/universe was fine tuned for their version of life.
Sure intelligent life could exist under different conditions. Quantum physics permits many configurations. The question really is, is the universe fine tuned to maximise the emergence of intelligent life? Or more correctly, how close to maximum probability is it? It certainly seems pretty close to maximum probability, given a uniform, or near uniform, distribution for the values of the different constants we use in the laws of physics. We can envisage many planets and many universes that would be very unhospitable to life, but that isn't to say that the emergence of life within them would be impossible. As you correctly suggest any life that does emerge is adapted to its environment, but also the enviroment seems well adapted to the emergence of life.

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Ken G
Gold Member
That's right, and the big question is, is there really a scientific question there? Just because I can pose a question does not guarantee that science has a means of answering it. For example, "why does science work?" is obviously a question that science cannot answer! So what about "why are the constants what they are?" I think the only way would be to find another theory that leads to those constants in that other theory, but why wouldn't that other theory also have constants in it? All of our theories have so far...

Chronos