When Was the Universe's Expansion Rate Zero?

[ChrisVer]

a) I really can't comment in great detail. I don't know the detailed history. My understanding was that Einstein put it into his equations specifically to stabilize the universe against collapse and for no other reason. I believe two things happened after that. 1) Hubble's results were interpreted as the expansion of the universe. 2) It was pointed out that the cosmological constant could not stabilize the universe, it was still subject to clumping. Einstein later declared the cosmological constant as 'my biggest mistake'. So, in effect he renounced it as part of GR! That I believe was generally accepted as correct, until other ideas popped up like inflation and until the discovery of acceleration of expansion.

You want to say that it was always consistent. It was always the same theory. Well historically I think you are wrong.
[...]
This depends upon what you define as GR. Einstein's original version with the kludged-in cosmological constant or the version in which the constant was for some time renounced.

Well, if you try to work out GR, you will find that the cosmological constant appears by itself as a constant. So it's not something that contradicts in any way the theory of GR. GR then contains the cosmological constant by itself, putting it to zero is just taking a more specific model and working on it, it's not changing GR. In any case if you think that two models make up different theories, then you are wrong.
To put it roughly: GR "stops" as a theory at Einstein's equations. After that, you are choosing a model. different models will give you different solutions for the Einstein equations, they won't give a different underlying theory.

OK, that's exactly what I meant. (Because lot's of physicists say so. GR has no concept of a quantum nature. If there something quantum about gravity you won't find it in GR.)

No matter what, the GR works in the regime we are talking about.

Well, if QM demands that GR breaks down at some scale, then yes they are incompatible aren't they?
Now you've said it for me. GR may not be a final theory (in fact it cannot be if QM holds), just as Newton's theory was not final. Einstein himself admitted to the possibility.

Yes they become incompatible at some point. Einstein himself renounced QM, I don't think his words have any credit ... well to get more serious, as Drakkith said, that makes no sense. Nobody is trying to work with GR in the scale where quantum effects are supposed to start working. At least not with GR as it is (maybe with LQG or something else).

 

[PeterDonis]

My understanding was that Einstein put it into his equations specifically to stabilize the universe against collapse and for no other reason.

Yes, he did. So what? That doesn't change the fact that, as a theory, GR naturally includes the cosmological constant. Einstein didn't realize that when he originally developed the field equation; then he was confronted with the fact that his original field equation didn't allow for a static solution for the universe, and he realized that the cosmological constant term could be added without violating any of the conditions he had assumed when he originally derived the field equation. In other words, his desire to find a static model caused him to discover that his own equation naturally included an extra term he hadn't considered.

I believe two things happened after that. 1) Hubble's results were interpreted as the expansion of the universe.

Yes. Although I'm not sure that was the first time an expanding model had been considered; IIRC Friedmann and others were already doing that well before Hubble's results were obtained.

2) It was pointed out that the cosmological constant could not stabilize the universe, it was still subject to clumping.

I'm not sure what you mean here by "clumping". The problem with the Einstein static universe, as a model, is that it is unstable, like a pencil balanced on its point. A small perturbation can cause it to either expand forever, or collapse into a singularity. Which one will happen depends on the perturbation.

Einstein later declared the cosmological constant as 'my biggest mistake'. So, in effect he renounced it as part of GR!

Yes, but that doesn't mean he was right. Nor does it mean that all other physicists doing research in GR agreed with him. GR is not "whatever Einstein says it is".

That I believe was generally accepted as correct

I don't think so. As I mentioned before, cosmologists continued to give estimates for the value of the cosmological constant all along; it was just that, until (IIRC) the mid-1990's, the value "zero" was always within the error bars, so it was possible to maintain that the model without the cosmological constant fit the data. Once the error bars were narrowed enough to exclude the value "zero", it was no longer possible to do that. But that's a matter of model selection, not the underlying theory; the underlying theory always included the cosmological constant.

Also, even on the purely theoretical side, models with a nonzero cosmological constant were being researched--for example, de Sitter spacetime.

You want to say that it was always consistent. It was always the same theory. Well historically I think you are wrong.

I've commented on the historical part above. But also, I don't think this is purely a historical question. Considered purely as a logical structure, GR naturally includes the cosmological constant. The fact that not all physicists have always realized that does not change this, not even if one of those physicists was Einstein.

the measurements indicating acceleration, while significant, are not highly precise.

True, but that uncertainty, as I understand it, is why there are still error bars around the value of the cosmological constant. But the fact that a model with a cosmological constant exactly equal to zero no longer fits the data--i.e., the fact that the error bars no longer include the value "zero"--is, AFAIK, well established. This is probably worth a separate thread, though, since there are those here on PF that are much more familiar with the recent literature in this area than I am.

If there something quantum about gravity you won't find it in GR.

Agreed. GR is a purely classical (non-quantum) theory.

This depends upon what you define as GR.

I guess so, but I don't see an argument over definitions as very fruitful. My point is that, as I said above, the logical structure that leads you to the Einstein Field Equation results in the cosmological constant naturally being included in that equation. Whether or not that particular logical structure (rather than a different, less natural one where you exclude the cosmological constant by fiat) is what you want to call "GR" is a question of words, not physics. I'm interested in the question of physics.

if QM demands that GR breaks down at some scale, then yes they are incompatible aren't they?

Only if you think GR is a final theory. If GR is just an approximation, then it is no more incompatible with QM than Newtonian gravity is incompatible with GR.

A theory that changes is not precisely the same theory.

The theory didn't change; the model changed. A single theory can lead to many different models, since there are many different particular solutions of the equations of the theory.

Without any prediction of the value of the cosmological constant, it's not predictive in a useful sense anyway.

If this is your standard, then we don't have any theories that are "predictive in the useful sense". Every single physical theory we have, or have ever had, has had parameters that had to be input by hand because the theory could not predict their values. QM has the same problem; our current Standard Model of particle physics, for example, has something like 26 free parameters that have to be put in by hand.

You know, I wonder why we're even arguing about this because it is a small point. You believe that GR never changed and I don't. So what?

Reading back through the thread, I think what I was objecting to originally was your use of the term "breakdown of mainstream physics" in reference to models including a cosmological constant. I think that's way too strong, particularly if you are basing it on a historical interpretation that may only apply to certain physicists (like Einstein) rather than on the internal logic of the theory itself (which I talked about above).

I wasn't asking when it dominated, but rather was it there from the start? The later is probably unanswerable.

Yes, because, even if we just consider the post-inflationary period (since inflation raises a whole new set of issues), until the cosmological constant starts dominating the dynamics, there's really no way to detect its presence. All we really have at that point is the assumption that, at least since the start of the post-inflationary period, the cosmological constant has indeed been constant. That assumption has some grounding in quantum field theory (basically, that if the vacuum state of the universe had changed it would have had other effects that we would have seen), but I agree that there doesn't seem to be any way to test it experimentally, at least not in the near future.

Do you really think cosmology is settled, wrapped up with a neat little bow?

Certainly not, and I haven't meant to imply that it is. But I think that the existence of a nonzero cosmological constant in our current universe is fairly well settled (with the caveats I gave above--again, I think this is worth a separate thread on that specific question).

Well, does the theory say it's a constant or not?

Yes; more precisely, what I have been saying is "naturally" part of the Einstein field equation is a constant (i.e., no variation in space or time) times the metric tensor (which is what the term "cosmological constant" is standardly used to refer to).

We do know that the theory does not define it's value (although I'm not sure).

Correct, the field equation I referred to just now can't tell you what the value of the constant is--any value (including zero) is consistent with the rest of the logic.

Did Einstein have a value in mind that would balance gravity?

I don't know, because I don't know if he had a specific value in mind for the density of ordinary mass-energy in the universe. But given the latter value, the value of the cosmological constant is determined, since it has to exactly balance the effect of the ordinary mass-energy.

Can you just say that some theory is right, alter it or limit it, and then still claim it was right all along?

When did I say GR was "right"? I am only trying to get clear about what we should count as "GR", in terms of the natural logical structure of the theory. I'm certainly not trying to claim that that natural logical structure must exactly match all present or potential future experimental data.

The only important point I would like to make is that we should not treat our theories as final

I agree. But we also need to realize that, even if our current knowledge is not final, it does limit the space of possibilities.

 

[CKH]

Well, if you try to work out GR, you will find that the cosmological constant appears by itself as a constant. So it's not something that contradicts in any way the theory of GR. GR then contains the cosmological constant by itself, putting it to zero is just taking a more specific model and working on it, it's not changing GR. In any case if you think that two models make up different theories, then you are wrong.
To put it roughly: GR "stops" as a theory at Einstein's equations. After that, you are choosing a model. different models will give you different solutions for the Einstein equations, they won't give a different underlying theory.

No matter what, the GR works in the regime we are talking about.

Your last statement is fine. However, in BBT we do apply it in regimes where we cannot possibly know for certain that it still holds (experimentally).

Yes GR works locally and we extrapolate with it (quite fairly) beyond it's known verification. However to say it's correct even if it isn't in some regime is just like saying Newton's theory is correct. The only difference is that we know for sure that Newton's theory is not correct in all cases while we only suspect that GR cannot be correct in all cases.

We argue about how you evaluate the "correctness" of a theory. Looking back at my messages I feel I'm guilty picking nits so let's not go crazy over this issue.

Yes they become incompatible at some point. Einstein himself renounced QM, I don't think his words have any credit ... well to get more serious, as Drakkith said, that makes no sense. Nobody is trying to work with GR in the scale where quantum effects are supposed to start working. At least not with GR as it is (maybe with LQG or something else).

He did not "renounce" QM. QM is an empirical theory that unfortunately lacks a physical (or if you like, a metaphysical) explanation. What he actually claimed was that QM is an incomplete theory, in other words, it remains mysterious. I happen to agree.

Richard Feynman said something to the effect that "the central mystery of QM is the wave/particle duality" and implied that this mystery is impenetrable. That's why I consider it an empirical theory. It has some equations that correctly predict experiments, but it has no sensible explanation as yet.

These days "physics" appears to have turned into accounting: "shut up and calculate" and "physics is the equations". If that's all that physics is, it's rather unilluminating and disappointing for it has abandoned the pursuit of understanding nature.

 

[PeterDonis]

Richard Feynman said something to the effect that "the central mystery of QM is the wave/particle duality" and implied that this mystery is impenetrable. That's why I consider it an empirical theory. It has some equations that correctly predict experiments, but it has no sensible explanation as yet.

These days "physics" appears to have turned into accounting: "shut up and calculate" and "physics is the equations". If that's all that physics is, it's rather unilluminating and disappointing for it has abandoned the pursuit of understanding nature.

I sympathize with this point of view, but I would like to point out that it is based on an implicit assumption that "understanding nature" includes coming up with a "sensible explanation", by which I think you mean something like "an explanation that our intuitions tell us is sensible". But that assumes that there *is* such an explanation. What if there isn't? What if our intuitions about what is "sensible" simply aren't correct outside of a certain regime (basically the regime in which those intuitions originally evolved)? Perhaps that is why we end up having to express our physical theories using math: the math forces us to construct models that agree with experiments, even if our intuitions tell us they aren't sensible.

 

[CKH]

I have to admit to that possibility. For example, it's hard for us to imagine a 4-dimensional space in an intuitive sense. How can four lines be mutually orthogonal? But, it's not so hard to analyze with math. I used to think about this when I was a freshman (long, long ago). If we lived in a 4-dimensional space we could "see" every point within a three-dimensional object without any obstruction of our view. This would be handy for doctors but very hard to imagine.

I was reading yesterday that birds have 4 types of color cone cells in their eyes, while we have only three. How can we possibly imagine what colors they see?

In SR we have relativity of time and space, something outside of our experience. However in the LET view of relativity, there is a mechanical explanation

But, in QM we have something very strange (e.g. with Feynman's mystery of the wave/particle duality). In recent years a (French?) experimenter has found a physical model that behaves very much like the wave/particle duality. He uses a tray of silicone oil that is vibrated. Drops of silicone on the surface bounce creating waves around each drop. The drops can travel in uniform motion. The classic two slit experiment is done with the moving drops and an interference pattern emerges. It looks very much like QM. So at least for this mystery of QM, their is hope for a mechanical understanding.

 

[Torbjorn_L]

Some of the later discussion is confusing (at least to me), since Strassler's image respond to a lot of the mentioned details and questions.

Especially the existence of a singularity is early speculation, and rejected by today's inflation cosmology. There isn't a singularity where it was predicted to be. (See my first comment.)

I note that bouncing cosmologies are also rejected by today's cosmology. So they have to replace it with better prediction, an extraordinary proposal at this time.

@Niramas:

But how do we know that the current laws of physics do not break down as we extrapolate back to the inflation era?

We don't know that yet. But the predictive survival of quantum fluctuations those imprints show up in the cosmoc microwave background and in structure formation (matter/dark matter filaments that become galaxy clusters) means physics is good during that period.

As the image show, there isn't any problem with so called semi-classical physics (quantum field theory on a background of weak gravity) as such.* But who knows?

* There are theorems that show as you go back you are heading for a breakdown.

- In effect, the redshift of field fluctuations (particles) moving forward becomes blueshift going backwards, under semi-classical conditions. But those breakdowns may be non-existent in practice, since you have no upper limit on inflating geodesics. BICEP2 certainly suggested that the energy density was finite (and well under Planck mass) for quite a while (an expansion factor of perhaps 10^10 000, according to some theory papers).

- The de Sitter spacetime that inflation approximates have a topological bottleneck. But again, this is theory and there are ways to make it go away. YMMV.

I'm with vociferous here. As long as we see isotropy, I'm good.

If the expansion of the universe has slowed before, why is just assumed the the current acceleration will continue indefinitely? It seems to me a precarious assumption.

It isn't an assumption, it is an observation (as you note) and a prediction from inflationary standard cosmology (which appeared after WMAP -04).

@vociferous:

Since we do not have predictive models of what happened immediately following the big bang, it simply makes no sense to reference time before the big bang.

It makes sense to reference time before the HBB in inflation.

@steve2k:

So, just out of curiosity, is anyone willing to take the PRESENT rate of expansion, and calculate back to the time of expansion = 0?

Please.

I described where you could find such calculations - they are lengthy because of the various eras with different functions describing expansion rate evolution - and why there isn't any "time of expansion = 0" in current theory.

 

[Torbjorn_L]

These questions seems OT, but I'll respond here anyway:

If there something quantum about gravity you won't find it in GR.

Agreed. GR is a purely classical (non-quantum) theory.

I note though that you can say that if there is something quantum in electromagnetism you won't find it in EM. However, when you quantize it (by way of its Lagrangian) you get quantum electrodynamics - QED - including photons.

Similary you can perfectly well quantize GR (by way of its Lagrangian) and get a QGR, including gravitons consistent with later string theory. However, observations of gravitons are loosley constrained (slowing spin in pulsar binaries) and the theory breaks down when you get away from semiclassical conditions. E.g. when gravity is strong/scales are small, so GR can no longer be approximated by a linear quantum field and its non-linearities kicks in.

But, in QM we have something very strange (e.g. with Feynman's mystery of the wave/particle duality). --- a tray of silicone oil that is vibrated.

Quantum mechanics has no inherent "wave/particle duality", it went away with quantum field theory which is what you get when you add relativity to non-relativistic QM. It is more correct to say that particles are ripples ("waves") in a field.

Also, adding relativity means you get non-local correlations separated from local causality. That is IMHO less of a degeneracy, more clarifying, but YMMV.

The latter part describes a pilote-wave model, which also breaks down when you add relativity as in quantum field theory.

 

[SteveK2]

Some of the later discussion is confusing (at least to me), since Strassler's image respond to a lot of the mentioned details and questions.

Especially the existence of a singularity is early speculation, and rejected by today's inflation cosmology. There isn't a singularity where it was predicted to be. (See my first comment.)

I note that bouncing cosmologies are also rejected by today's cosmology. So they have to replace it with better prediction, an extraordinary proposal at this time.

@Niramas:
We don't know that yet. But the predictive survival of quantum fluctuations those imprints show up in the cosmoc microwave background and in structure formation (matter/dark matter filaments that become galaxy clusters) means physics is good during that period.

As the image show, there isn't any problem with so called semi-classical physics (quantum field theory on a background of weak gravity) as such.* But who knows?

* There are theorems that show as you go back you are heading for a breakdown.

- In effect, the redshift of field fluctuations (particles) moving forward becomes blueshift going backwards, under semi-classical conditions. But those breakdowns may be non-existent in practice, since you have no upper limit on inflating geodesics. BICEP2 certainly suggested that the energy density was finite (and well under Planck mass) for quite a while (an expansion factor of perhaps 10^10 000, according to some theory papers).

- The de Sitter spacetime that inflation approximates have a topological bottleneck. But again, this is theory and there are ways to make it go away. YMMV.

I'm with vociferous here. As long as we see isotropy, I'm good.
It isn't an assumption, it is an observation (as you note) and a prediction from inflationary standard cosmology (which appeared after WMAP -04).

@vociferous:
It makes sense to reference time before the HBB in inflation.

@steve2k:
Please.

I described where you could find such calculations - they are lengthy because of the various eras with different functions describing expansion rate evolution - and why there isn't any "time of expansion = 0" in current theory.

 

[SteveK2]

Wow! Talk about inability to think outside the box! (referring to refusal to do the simple calculation regarding expansion of the universe) I don't care what the theory is, I just want to know, out of simple scientific curiosity, how far back in time you would have to go for the expansion rate of the universe to be zero, assuming the PRESENT rate of expansion has always occurred (at least always occurred from the time calculated to have started by conducting the simple extrapolation; yes, I don't want to have to re-learn my math from 30 years ago, and look up whatever the expansion rate is, etc., I figured that one of you physics geniuses could do this in a matter of seconds. I really have to wonder if you people are afraid of doing this at this point.

 

[PeterDonis]

I just want to know, out of simple scientific curiosity, how far back in time you would have to go for the expansion rate of the universe to be zero

Never, because the rate was never zero. In a model where there is no inflation and the universe starts out with an initial singularity, the expansion rate as you go back in time towards the singularity increases without bound; it doesn't decrease. In a model where there is inflation, once you're far enough back in time to be in the inflation era, the expansion rate does decrease exponentially (as you go back in time), but it never reaches zero (and anyway quantum effects are assumed to come into play at some point so the concept of "expansion" is no longer valid back past a certain point).

However, all of that is really beside the point, because your question as you ask it doesn't even make sense:

assuming the PRESENT rate of expansion has always occurred

If the present rate has always occurred, how can there ever have been a time when it was zero? Your question makes an assumption that's inconsistent with what you're asking.

Perhaps you really meant to ask, if we extrapolate the present rate of expansion backward, when does the size of the universe go to zero? I already answered that way back many posts ago: it's just the Hubble time. I posted a link for that before, but here it is again:

http://en.wikipedia.org/wiki/Hubble's_law#Hubble_time

Quoting from that Wikipedia article: "The value of Hubble time in the standard cosmological model is $4.35 \times 10^{17}$ s or 13.8 billion years."

 

[PeterDonis]

I believe the extrapolation would be dramatically fewer years ago than when the "Big Bang" is theorized to have occurred.

As you can see from the quote at the end of my previous post, this is not the case.

 

[SteveK2]

Ok, I didn't think I would have to explain this to get an answer. Let's pretend the Universe is a balloon. Let's pretend that long ago, the balloon was deflated. Let's pretend that this universal balloon began filling with air (dark matter, or whatever you want to fill it with). If the air was filling the balloon at a constant rate, the rate of expansion would decrease over time. (the rate of radius increase of the balloon would decrease). If air was added at a sufficient exponential increase, the rate of radius increase would be constant). Now let's increase the rate of air increase even higher, so that that radius increases even faster than a constant increase. If we can measure the increasing rate that the radius increases, then it is a simple mathematical calculation to determine how long ago the radius was equal to zero. Now let's move to our present, actual universe. No theory, no constraints, no Hubble this or Hubble that. It's just a matter of taking the present, known radius of the universe (if it's not spherical, just an average radius will be fine), taking the present, measured rate of acceleration of the expansion of the universe, and doing the calculation to determine when r=o. Very simple. If nobody wants to do this simple calculation, then please just post the present known radius of the universe (average radius), and the present known acceleration rate of the expansion of the universe and I'm pretty sure I can refresh my math of 30 years ago and do the math. Thank you.

 

[PeterDonis]

If the air was filling the balloon at a constant rate, the rate of expansion would decrease over time. (the rate of radius increase of the balloon would decrease).

In other words, if the rate of increase in volume is constant, the rate of increase in radius decreases. Yes, this makes sense, for a balloon. But the universe is not a balloon, and does not behave like one. See below.

It's just a matter of taking the present, known radius of the universe

Which is infinite, according to our best current estimate, because the universe is not spatially closed. Also, the universe, spatially, is not a 3-dimensional object with a 2-dimensional "surface", like a balloon. It's a 3-dimensional space with no boundary at all.

the present, measured rate of acceleration of the expansion of the universe

Which is not the rate at which "air" (or "space" or anything else) is being "added" to the universe, or the rate at which that rate is changing, etc. It's just the rate at which the recession velocities of galaxies a given distance apart are increasing. It certainly isn't the "rate of radius increase" of the universe, because the radius is infinite, and the universe doesn't have a boundary at all, as above. So I don't know what number to give you.

 

[SteveK2]

okay, I guess I'll just have to do it myself. I'm pretty sure I have seen an estimate of the size of the universe, so I can find that (unless you have that handy). All I need is the PRESENT acceleration of the universe. I am truly amazed at this discussion! It would be like someone asking me, a PhD in Marine Science, some basic question on oceanography. I really thought this was a basic thought experiment with a quick an easy solution, not necessarily meaningful, or "according to theory", but easy to produce. I believe there is a reason why it has been so difficult, but I'll save that for possibly later.

 

[Matterwave]

okay, I guess I'll just have to do it myself. I'm pretty sure I have seen an estimate of the size of the universe, so I can find that (unless you have that handy). All I need is the PRESENT acceleration of the universe. I am truly amazed at this discussion! It would be like someone asking me, a PhD in Marine Science, some basic question on oceanography. I really thought this was a basic thought experiment with a quick an easy solution, not necessarily meaningful, or "according to theory", but easy to produce. I believe there is a reason why it has been so difficult, but I'll save that for possibly later.

The current best estimate for the size (radius) of the universe is $\infty$ meters. The current best estimate for the expansion rate is given by the Hubble constant $H_0 \approx 70(km/s)/Mpc$, the current best estimate for the deceleration parameter is $q_0\equiv -\left.(1+\dot{H}/H^2)\right|_{t=t_{now}}\approx -1\pm .4$. Extrapolate away.

 

[PeterDonis]

I'm pretty sure I have seen an estimate of the size of the universe

If you find one that's not $\infty$, please post it, it will be of great interest. Be sure it's an estimate of the size of the entire universe, not just the observable universe, though.

 

[PeterDonis]

I am truly amazed at this discussion! It would be like someone asking me, a PhD in Marine Science, some basic question on oceanography.

It may seem that way to you, but remember that, in this situation, we are the ones in the position of the PhD, not you, and what seems like a "basic question" to a person not knowledgeable in a field might not seem that way to someone who is knowledgeable. To us, this discussion is not like someone asking a basic question, like "what is the volume of Earth's oceans". It's like someone asking a question that actually doesn't make sense at all, like "what is the elasticity of Earth's oceans". And then, when you point out that the oceans are liquid, not solid, and don't have an elasticity, the person says, "look, forget about your model that says the oceans are liquid, just give me the parameters of Earth's oceans and I'll calculate the elasticity myself".

 

[Drakkith]

Thread closed for moderation.

 

[Drakkith]

Since the OP's question has been answered more than once, this thread will remain closed.