When Was the Universe's Expansion Rate Zero?

[SteveK2]

I have been wondering for a few years if the current equations for the expansion of the universe have ever been used to extrapolate back in time, to determine how many years ago, the rate of expansion was zero. I believe this amount of time will not agree with the accepted age of the universe. Does anyone here know if this seemingly simple calculation has been performed? (I'm a geologist, and a little lazy :), and most importantly, not a math wiz, so I'm trying to avoid having to attempt it myself)

 

[jedishrfu]

Welcome to PF!

I'd suggest you read up on it first before asking this kind of question:

http://en.wikipedia.org/wiki/Big_Bang

You're making the assumption that time is linear and absolute for the universe as a whole whereas the current view is that time began with the big bang and that we can't know what occurred before it.

If you look at the image you can see that the universe went through an extreme expansion within a very small time period:

 

[SteveK2]

No assumptions made. In fact, you seem to assume that such a back extrapolation would extend before the "Big Bang". I believe the extrapolation would be dramatically fewer years ago than when the "Big Bang" is theorized to have occurred. I think most astrophysicists are afraid to do this extrapolation, because it may just blow their minds!

 

[Drakkith]

I have been wondering for a few years if the current equations for the expansion of the universe have ever been used to extrapolate back in time, to determine how many years ago, the rate of expansion was zero.

The expansion rate was never zero, so we can't extrapolate backwards in time to that point. As we look backwards in time, the expansion rate gets larger, not smaller. This means that the rate of expansion has been slowing over time up until about the present day when the density of the universe fell below a critical value and dark energy began to dominate and accelerate the expansion.

Also, be aware that the big bang is the point in time that our calculations stop giving useful predictions and start generating infinities, so we can't extrapolate backwards past this point in time.

 

[jedishrfu]

Please keep in mind that PF does not discuss speculative science or personal theories. Our mission is to discuss mainstream science and math in the context of helping students learn.

 

[vociferous]

No assumptions made. In fact, you seem to assume that such a back extrapolation would extend before the "Big Bang". I believe the extrapolation would be dramatically fewer years ago than when the "Big Bang" is theorized to have occurred. I think most astrophysicists are afraid to do this extrapolation, because it may just blow their minds!

It does not matter what you believe. It only matters what you can show. We do this through a combination of proofs and empirical observations. Hubble Time has been well-proven in cosmological literature and the proofs of the Hubble Time that line up with empirical observation put the age of the Universe at about 13.8 billion years.

I suggest reading Introduction to Cosmology by Barbara Ryden. The text is written at an upper division undergraduate level so it should be fully accessible to anyone in the physical sciences since presumably everyone has the same basic lower division mathematical classes to graduate (Vector Calculus, Linear Algebra, Ordinary Differential Equations). Even if your math is a little rusty, you should still be able to follow along.

It is futile to come up with your own theories about the age of the universe and how to calculate it until you understand the basics. The answer is, yes we do estimate the age of the universe by extrapolating backwards, but you have to understand the mathematical proofs and how they relate to real empirical evidence to understand how to create a model of the age of the universe. Furthermore, studying this goes back to the Friedman equation in 1922 and the number of models and arguments put forward since then is enormous. Anything you can think of, someone else has probably considered. You need a deep understanding of cosmology to contribute something useful at this point.

 

[Torbjorn_L]

Actually I think Susskind's youtube Stanford lectures on cosmology handles it with "Vector Calculus, Linear Algebra, Ordinary Differential Equations". They are free, and what you don't know he has other free lectures to get a grasp with. That is ~ 20 h of material. [Note: You want the youngest, most update series, he has done at least 2 by now!]

In the interest of avoiding speculative science and other confusion, I want to remind that confusingly "big bang" has no set definition.

******

Okay, I don't know if the rest is more confusing than helping. But let me post it anyway in case it helps. (This forum is moderated for clarity, right?)

It is perhaps wise to use the precise and conservative Hot Big Bang era definition, which if still has a bit of speculative physics (but less so than the rest of the definitions, thus conservative) at least avoids potential historical and thermodynamic confusion. See here for a well known high energy physicist describing the various definitions and the reliability of physics for various eras:

[ From http://profmattstrassler.com/2014/03/26/which-parts-of-the-big-bang-theory-are-reliable/ ]

If Inflation precedes, as described in the BICEP2 "History of the universe" image, the historical confusion is that one push a new era in front of observed BB. (Observed in the cosmic microwave background spectra, say.) The thermodynamic confusion is that this process cooled the universe towards 0K whatever its starting temperature. Until it ended and the release of remaining potential energy of the process heated it up, it was a (relatively or perhaps absolutely) Cold Inflation era.

The HBB era definition has also the possible advantage of that there wouldn't be any non-removable infinities or "beginnings of time" involved in the HBB of standard cosmology (Lambda-Cold Dark Matter cosmology), if BICEP2 is correct. The energy scales involved is then 100 times lower than such breakdown.

Interestingly in this context of time vs expansion rate, note in the logarithmic scale BICEP2 image that inflation, if it exists, goes exponentially. It is therefore a much _slower_ rate process than expected from a presumably superexponential behavior of a 'generating infinities in our theories big bang'.* Just extend the max slope trend from the exponential towards the symmetry plane and it hits it way before the image "Big Bang". This is where the classical "Big Bang" should lie!

That makes sense, it is some models that break down, not the physics necessarily. [I 'know' there is a paper on this observation, but I can't find it as I write. :-/ Fortunately cosmologist Ethan Siegler comes to my rescue with a similar, safer analysis out of existing cosmology:]

"What inflation — our best scientific theory as to what preceded the [Hot] Big Bang — tells us about “what came before the Big Bang” is, perhaps, very surprising. If the Universe was filled with matter (orange) or radiation (blue), as shown above, there must be a point at which these infinite temperatures and densities are reached, and thus, a singularity. But in the case of inflation (yellow), everything changes."

[From http://scienceblogs.com/startswithabang/2012/10/15/what-happened-before-the-big-bang/ ]

So how far back goes the exponential-so-never-zero-expansion-rate Cold Inflation? This is where we have *no* data yet and *only* speculations... [See Strassler's image.]

* Yes, I know that this isn't the same as declaring, erroneously, that "Big Bang" is necessarily a singularity. But it is morally the same, and that breakdown is where the superexponential behavior would come from as I understand it.

 

[Niramas]

The working backwards to the era of inflation seems an incredible achievement to my puny Engineer's brain. But how do we know that the current laws of physics do not break down as we extrapolate back to the inflation era? That would seem to be more likely than to actually approach a singularity, IMO.

(sorry if off-topic, but the question just comes to mind)

 

[vociferous]

The working backwards to the era of inflation seems an incredible achievement to my puny Engineer's brain. But how do we know that the current laws of physics do not break down as we extrapolate back to the inflation era? That would seem to be more likely than to actually approach a singularity, IMO.

(sorry if off-topic, but the question just comes to mind)

We do not know. You have to make certain assumptions, such as the geometry of the universe, which may or may not be valid. One of the only axioms of physics (really all science) is to assume isotropy until it is disproved. It is as simple as that. There are a lot of different possible models of cosmology. It just comes down to which models that best fit the evidence are the most isotropic. Those are the ones we generally conclude are the most correct.

When NASA sends a probe to Jupiter, they assume gravity works the same there as it does near Earth. If the laws of physics immediately following the Big Bang were fundamentally different, like 1+1=3 and gravitational force increased proportional to the cube of the distance, then we will probably never be able to figure out what happened. However, the fact that current models so closely fit our observations suggests that many if not all of the assumptions are either correct or at least reasonably accurate.

 

[CKH]

Why even assume that time starts when the backward projected energy density reaches infinitely. Couldn't time have started with an existing finite density, e.g. after the conjectured inflation occurred.

That the density is ever increasing in the past is a conjecture. It's an extrapolation from what we see today, but not necessarily correct. In bounce theories, it is not correct.

 

[vociferous]

Why even assume that time starts when the backward projected energy density reaches infinitely. Couldn't time have started with an existing finite density, e.g. after the conjectured inflation occurred.

That the density is ever increasing in the past is a conjecture. It's an extrapolation of what we see today, but not necessarily correct. In bounce theories, it is not correct.

I don't believe that current models have anything to do with "time starting". They simply use the singularity as a frame of reference. 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.

Also, that density is increasing in the past (I'm assuming you mean mass density) is not a conjecture. It is a model, and it happens to be the model that currently best fits the evidence.

Popper is the one who really defined how conjectures related to science. It implies that your idea is so unrefined that you are not even able to test it. Current models are far past the conjecture stages. They are testable hypotheses that have been pretty well-corroborated.

 

[ChrisVer]

Well that energy density was not always rising as you go in the past, it does drop however after the end of inflation to the values today.
During inflation you only had a finite constant energy density-negative pressure (so there should be some mechanism which moves us from inflation to radiation and matter dominated universe eras, and thus to reheating of the universe).
Also I have an idea that bounce theories are not accepted. But in this I may be wrong.
http://www.damtp.cam.ac.uk/user/db275/TEACHING/STRINGS/Basics.pdf

 

[CKH]

I don't believe that current models have anything to do with "time starting". They simply use the singularity as a frame of reference. 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.

That's convenient to avoid the issue of what happened prior to the Big Bang, but not very convincing. I've heard this sort of argument but it is not a consistent one. We use measurable conditions (e.g. of the CMB and present conditions) and assume that there was a time before the CMB and that we can calculate the density as far back in time as we like. But when things get tough (impossible to calculate or nonsensical) then we are allowed to assert that there is no time before the BB to avoid the issue?

Also, that density is increasing in the past (I'm assuming you mean mass density) is not a conjecture. It is a model, and it happens to be the model that currently best fits the evidence.

I don't deny that. Where the conjecture comes into our model is in assuming that there exists a time before the earliest time from which we have actual data and that we can correctly extrapolate conditions at any time before that.

We go so far as to hypothesize that the universe approached infinite density at a finite time in the past. While that is tenable hypothesis, it is not necessarily true. But if it is true, then it is inconsistent to avoid asking what happened before that time. It's a sort of cop-out.

People often argue "BBT is only about the expansion of the universe. It doesn't say anything about the start of the expansion." That's fine, but it still begs the scientific question of what did happen before. Ignoring that problem is to ignore a legitimate question about nature. I might as well claim that there is no time before origin of the CMB and that the CMB is the condition in which the universe started.

Popper is the one who really defined how conjectures related to science. It implies that your idea is so unrefined that you are not even able to test it. Current models are far past the conjecture stages. They are testable hypotheses that have been pretty well-corroborated.

Just because we have models that work insofar as we know, does not imply that they are in fact correct (e.g. Newton's laws). We must be open to the possibility that our extrapolation is actually incorrect.

Bounce models (even though not mainstream) have the advantage over straight BB that you can ask what happened before expansion began and come up with an answer. There are plenty of papers published about bounce cosmology. The subject has scientific legitimacy even if it's not popular among BB theorists.

BB theorist admit that the physical laws we know of break down at really high densities so they cannot in the same breath rule out bounce models even if they don't like them.

 

[vociferous]

That's convenient to avoid the issue of what happened prior to the Big Bang, but not very convincing. I've heard this sort of argument but it is not a consistent one. We use measurable conditions (e.g. of the CMB and present conditions) and assume that there was a time before the CMB and that we can calculate the density as far back in time as we like. But when things get tough (impossible to calculate or nonsensical) then we are allowed to assert that there is no time before the BB to avoid the issue?



I don't deny that. Where the conjecture comes into our model is in assuming that there exists a time before the earliest time from which we have actual data and that we can correctly extrapolate conditions at any time before that.

We go so far as to hypothesize that the universe approached infinite density at a finite time in the past. While that is tenable hypothesis, it is not necessarily true. But if it is true, then it is inconsistent to avoid asking what happened before that time. It's a sort of cop-out.

People often argue "BBT is only about the expansion of the universe. It doesn't say anything about the start of the expansion." That's fine, but it still begs the scientific question of what did happen before. Ignoring that problem is to ignore a legitimate question about nature. I might as well claim that there is no time before origin of the CMB and that the CMB is the condition in which the universe started.



Just because we have models that work insofar as we know, does not imply that they are in fact correct (e.g. Newton's laws). We must be open to the possibility that our extrapolation is actually incorrect.

Bounce models (even though not mainstream) have the advantage over straight BB that you can ask what happened before expansion began and come up with an answer. There are plenty of papers published about bounce cosmology. The subject has scientific legitimacy even if it's not popular among BB theorists.

BB theorist admit that the physical laws we know of break down at really high densities so they cannot in the same breath rule out bounce models even if they don't like them.

I don't see it as avoiding the issue. It is simply that science has limits, and right now we simply do not have the physics to clearly describe what happened before, during or immediately after the big bang. That is what makes science special. It does not pretend to have all the answers. Until someone can create a testable theory, it is something like educated conjecture.

Also, pretty much everything you are talking about is already "built-in" to science. Cosmologists don't pretend like the Big Bang, or any other theory was carved into a stone tablet on Mount Sinai. The Big Bang simply fits the empirical evidence the best. If that changes in light of new evidence, then scientific opinion will change.

 

[Drakkith]

That's convenient to avoid the issue of what happened prior to the Big Bang, but not very convincing. I've heard this sort of argument but it is not a consistent one. We use measurable conditions (e.g. of the CMB and present conditions) and assume that there was a time before the CMB and that we can calculate the density as far back in time as we like. But when things get tough (impossible to calculate or nonsensical) then we are allowed to assert that there is no time before the BB to avoid the issue?

No one's avoiding the issue. We just don't have any information on what the conditions of the universe were prior to the big bang. And that's assuming something existed prior to the big bang. There are various theoretical models that predict something prior to t=0, but most if not all of those models are based upon theoretical physics that haven't been proven to be correct yet. (Such as string theory) Note that t=0 doesn't mean that we have assumed that time starts there, it's just placing the start of a counter at that point so we can measure the elapsed time since then.

I don't deny that. Where the conjecture comes into our model is in assuming that there exists a time before the earliest time from which we have actual data and that we can correctly extrapolate conditions at any time before that.

We go so far as to hypothesize that the universe approached infinite density at a finite time in the past. While that is tenable hypothesis, it is not necessarily true. But if it is true, then it is inconsistent to avoid asking what happened before that time. It's a sort of cop-out.

People often argue "BBT is only about the expansion of the universe. It doesn't say anything about the start of the expansion." That's fine, but it still begs the scientific question of what did happen before. Ignoring that problem is to ignore a legitimate question about nature. I might as well claim that there is no time before origin of the CMB and that the CMB is the condition in which the universe started.

Again, no one is ignoring the question. But without any sort of information on the conditions of the very early universe, there is no way to make a useful model that can be verified. What's the point of developing hundreds of possible models, none of which can be verified? It's a waste of time.

BB theorist admit that the physical laws we know of break down at really high densities so they cannot in the same breath rule out bounce models even if they don't like them.

Bounce models are ruled out because the universe doesn't appear to be cyclic in this way since the expansion of the universe is accelerating, not slowing. It has nothing to do with "not liking them".

 

[Drakkith]

That the density is ever increasing in the past is a conjecture. It's an extrapolation from what we see today, but not necessarily correct. In bounce theories, it is not correct.

Even in bounce theories, the density increases in the past at least until you get to the big bang. No one claims that the density continues to increase past this point.

 

[Niramas]

Bounce models are ruled out because the universe doesn't appear to be cyclic in this way since the expansion of the universe is accelerating, not slowing. It has nothing to do with "not liking them".

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.

 

[ChrisVer]

The dynamics of (de)accelerating are given by the Friedmann equations and they depend on the possible energy densities.

 

[Niramas]

The dynamics of (de)accelerating are given by the Friedmann equations and they depend on the possible energy densities.

And gravity was once explained by Newton's equations. This doesn't answer the question, which is more philosophical in nature than mathematical.

 

[ChrisVer]

That is nonsense.
I'm saying that nobody makes that assumption you referred to- nobody said that the universe is accelerating or decelerating [except for the experiment- and so we have the values we do for the energy densities]...It's a result of the assumptions we have put on the universe (those related to the choice of FRW cosmology) and General relativity. Doesn't GR hold?

 

[CKH]

Bounce models are ruled out because the universe doesn't appear to be cyclic in this way since the expansion of the universe is accelerating, not slowing. It has nothing to do with "not liking them".

I pretty much agree with the responses to my challange. Those response are much more fair than the claim that "time started at the BB".

Is it possible that physics of BBT will always be blocked by the singularity assumed in theory because mathematics itself is blocked?

At one time, not so long ago, we assumed that the expansion was slowing down. Now to our surprise it appears to be speeding up. Even if this is real, we have thus far failed to explain it. Who can say what will happen later? Already I have seen papers suggesting that the rate of increase is slowing down.

Be careful what you rule out as possible. An admission of ignorance is safer than to claim something as "ruled out" that may in fact be true. I have to admit to dislike of the term "ruled out" since it always depends on assumptions that may themselves be false.

 

[CKH]

Even in bounce theories, the density increases in the past at least until you get to the big bang. No one claims that the density continues to increase past this point.

In bounce theories the density of the universe is bounded, while in BBT (as I understand it) it is not. That is an important distinction. Bounce theories offer mathematical "hope" since no singularity is involved.

 

[ChrisVer]

why isn't the BBT density bounded?

 

[CKH]

why isn't the BBT density bounded?

I assumed that it isn't because the theory (as I understand it) puts no limit on the density. In the related theory of inflation, there are speculations about what happened at 10^-37 seconds when the universe was already expanding according to BBT. Was it not expanding at 10^-100) seconds according to the theory? Or at any exponent, according to the theory?

Maybe the BBT has changed or I never understood it properly. In fact this is why (tongue in cheek) I suggested time started when the CMB originated. You can still have a form of the BBT in that case but I didn't think that the accepted theory includes such a possibility.

Can you explain your comment?

 

[ChrisVer]

I tried to say that during inflation there was only energy density coming from a constant (and so bounded).
And do you have the physics that are supposed to work at 10^-100? Because so far we don't have such a theory...the Planck time is as far as we can go, because from that point back you need quantum gravity -something that doesn't work fine yet.
CMB is not the start of time. CMB is the point where the universe became transparent to photons (before that it was something like a plasma- trapping photons, because photons were interacting with matter). We can't see anything that happened before CMB, but we can make some predictions about what was there before (which lead to the inflation era), and they can reproduce the CMB spectrum and the (so small) fluctuations in temperature.

 

[SteveK2]

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

 

[ChrisVer]

For me that would be "nonsense" to do... it's like saying take p=mv and take it to v=0.99c...

 

[PeterDonis]

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

Sure, this is just the Hubble time:

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

But, as ChrisVer says, this doesn't necessarily mean anything, since the rate of expansion has changed over time.

 

[CKH]

I tried to say that during inflation there was only energy density coming from a constant (and so bounded).
And do you have the physics that are supposed to work at 10^-100?

Oh that's what you meant. Sorry I missed that. It's not what I was referring to. Before inflation, what was happening to the energy density according to BBT?

If singularities are somehow manageable in physics, then BBT can be a physical theory, otherwise it begins with a miracle and expands thereafter.

Unless of course BBT does not claim a singularity where density is unbounded. That's what I thought we were talking about, not inflation which is a sort of an add-on to BBT. (Inflation apparently helps BBT through a problem. I'll ask about this in another thread.)

You say physics breaks down. Well it is already broken if inflation is real. No one has a tested theory for inflation (let alone a theory based on known physics). More than that, physics (GR) as we know it is broken if the expansion is accelerating. You can put the cosmological constant back into GR but a) that is a breakdown of mainstream physics and b) it doesn't look like it works.

A few posts back you asked "Doesn't GR hold?" If we believe our new measurements of expansion, perhaps it doesn't. GR is not written in stone. Even Einstein himself suggested it could be wrong after singularities (black holes) were deduced.

Please do not conclude that I am denying GR's agreement with experiment in saying that it might be "wrong". We say Newton's theories are "wrong" but we know they work very well in many cases.

 

[ChrisVer]

Well GR works in its regime and I was referring to that regime (solving the Friedman equations to find the energy densities for the observed universe acceleration, or seeing whether it accelerates or not is a GR thing and it works)... If you try to go beyond that regime, then you should expect divergences from your predictions. At the Planck Scale GR is not supposed to work in the same way it does classically, because quantum effects might arise. That's why someone before referred to string theory as a candidate to solve some stuff (but it lacks experimental support).

Inflation for me works fine... in fact I think it's a really consistent way to explain the horizon problem of CMB, as well as it's able to explain the small fluctuations in temperature.
Where did you read that GR is broken if expansion is accelerating? The cosmological constant exists- and in fact nowadays our universe is governed by it.

If I recall well, in this I might be wrong, it was the inflatons that created the matter and radiation and those inflatons existed during inflation (and so before).

 

[CKH]

Well GR works in its regime and I was referring to that regime (solving the Friedman equations to find the energy densities for the observed universe acceleration, or seeing whether it accelerates or not is a GR thing and it works)... If you try to go beyond that regime, then you should expect divergences from your predictions. At the Planck Scale GR is not supposed to work in the same way it does classically, because quantum effects might arise. That's why someone before referred to string theory as a candidate to solve some stuff (but it lacks experimental support).

As I understand it (as a layman) GR and QM are in conflict in their predictions. One or both are wrong about something. I don't know why a brilliant man like Hawking wastes his time trying to predict things (like evaporation of black holes) using two conflicting theories.

Inflation for me works fine... in fact I think it's a really consistent way to explain the horizon problem of CMB, as well as it's able to explain the small fluctuations in temperature.

OK. I'd like to discuss that in another thread. I'll start one tomorrow.

Where did you read that GR is broken if expansion is accelerating? The cosmological constant exists- and in fact nowadays our universe is governed by it.

I say that because the cosmological constant was abandoned by mainstream physics for decades and then resurrected to explain the acceleration. These are different versions GR. There has been some effort to test whether it is a viable explanation. Some papers indicate that the question is not settled. When exactly did it kick in? Inflation theory has the earmarks of a cosmological constant, but it's obviously not the same "constant" that theorist speak of to explain the current acceleration.

If I recall well, in this I might be wrong, it was the inflatons that created the matter and radiation and those inflatons existed during inflation (and so before).

You talk about such speculative physics as if it were established fact. I don't take it that seriously.

 

[PeterDonis]

You can put the cosmological constant back into GR but a) that is a breakdown of mainstream physics and b) it doesn't look like it works.

I don't think either of these claims is correct.

Regarding a), the fact that Einstein left out the cosmological constant in his original formulation of the field equations doesn't mean it doesn't belong there. It does. From the standpoint of the theory, what would require explanation is leaving it out, not putting it in.

Regarding b), I don't know what you're referring to. The current Lambda-CDM model, which includes a nonzero cosmological constant, matches observations. (But see further comments below, in response to your subsequent post.)

Please do not conclude that I am denying GR's agreement with experiment in saying that it might be "wrong". We say Newton's theories are "wrong" but we know they work very well in many cases.

If all you mean by "wrong" is "an approximation that works well within its domain of validity but is not exactly correct", that's fine. (But then I don't see why you think GR and QM are incompatible--see below.) But the thing you are saying is "broken", the cosmological constant, is within that domain of validity. It's true that GR, by itself, doesn't predict any particular value for the cosmological constant; but the fact of it being nonzero is well within GR's ability to model.

As I understand it (as a layman) GR and QM are in conflict in their predictions.

I'm not sure I would put it that way. I would say that, if you insist that GR and QM have to both be combined into a single "final theory" that is exactly correct, they seem to be incompatible. But if you view GR as a low-energy effective field theory--i.e., as the classical limit of whatever the correct theory of quantum gravity turns out to be--then GR and QM are perfectly compatible, because you're not treating GR as a "final theory", you're treating it as an approximation. As I understand it, this is the current mainstream view.

the cosmological constant was abandoned by mainstream physics for decades and then resurrected to explain the acceleration.

No, that's not an accurate description of what happened. What happened was that, for decades, a model with a zero cosmological constant was the best fit to the data. Then we got more and better data, and a model with a nonzero cosmological constant became the best fit to the data.

All during that time, cosmologists were taking measurements and using them to estimate the value of the cosmological constant. Nobody "abandoned" the concept; it was always there. But until the value "zero" was no longer within the error bars of the measurements (which happened, IIRC, sometime in the mid-1990s), nobody could say for sure whether it was actually present.

These are different versions GR.

No, they aren't. They're different particular models using the same underlying theory (GR). Just as a Newtonian model of the solar system that includes only the planets, and a Newtonian model of the trajectory of a baseball in Earth's gravity, are two different particular models using the same underlying theory (Newtonian mechanics). You wouldn't say that two such Newtonian models were "different versions" of Newtonian mechanics, would you?

Some papers indicate that the question is not settled.

References, please? What, exactly, is "not settled"?

When exactly did it kick in?

Asking when the cosmological constant began to dominate the universe's dynamics is very different from asking whether its value is zero or nonzero. The latter question is settled; it's nonzero.

Inflation theory has the earmarks of a cosmological constant, but it's obviously not the same "constant" that theorist speak of to explain the current acceleration.

Correct. Inflation theory requires that the vacuum state of the universe during the inflationary period was very different from the vacuum state of the universe today. Today's vacuum state has a very, very small (but nonzero) cosmological constant. The inflation vacuum had (if the theory is correct) a very, very large cosmological constant. GR can model both scenarios, at least as far as the dynamics of spacetime goes, but it can't explain why the cosmological constant should take one value rather than another, or why the value should change at some point. From the standpoint of GR, the value of the constant (and whether or not it changes at some point during the universe's evolution) has to be put in "by hand", so to speak, as an input to the model.

None of this poses any problem for GR, in and of itself. Whatever problems there are with inflation theory (and I'm not saying there aren't any; I am not familiar enough with the current literature in this area to assess that--and you said you were going to start a separate thread on that topic anyway, which I think is a good idea) have to do with issues that are outside the purview of GR.

 

[PeterDonis]

At the Planck Scale GR is not supposed to work in the same way it does classically

A better way to put this would be that, at the Planck scale, you can no longer make good predictions using a classical approximation like GR; you have to have an actual theory of quantum gravity. At that point you are no longer using GR.

 

[CKH]

I don't think either of these claims is correct.

Regarding a), the fact that Einstein left out the cosmological constant in his original formulation of the field equations doesn't mean it doesn't belong there. It does. From the standpoint of the theory, what would require explanation is leaving it out, not putting it in.

Regarding b), I don't know what you're referring to. The current Lambda-CDM model, which includes a nonzero cosmological constant, matches observations. (But see further comments below, in response to your subsequent post.)

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.

b) I cannot immediately give you a reference, I'll have to do a search. You should bear in mind that the measurements indicating acceleration, while significant, are not highly precise. So for the time being the lambda part of CDM may be relatively safe. Only time will tell. There are researchers who think that the acceleration may be an illusion caused by inhomogeneity. There are those who doubt that a constant lambda fits the data. There are also issues about dust, the interpretation of SN 1a light curves and selection effects. Research is ongoing to nail down the behavior of these supernova.

If all you mean by "wrong" is "an approximation that works well within its domain of validity but is not exactly correct", that's fine. (But then I don't see why you think GR and QM are incompatible--see below.)

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.)

But the thing you are saying is "broken", the cosmological constant, is within that domain of validity. It's true that GR, by itself, doesn't predict any particular value for the cosmological constant; but the fact of it being nonzero is well within GR's ability to model.

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.

I'm not sure I would put it that way. I would say that, if you insist that GR and QM have to both be combined into a single "final theory" that is exactly correct, they seem to be incompatible.

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

But if you view GR as a low-energy effective field theory--i.e., as the classical limit of whatever the correct theory of quantum gravity turns out to be--then GR and QM are perfectly compatible, because you're not treating GR as a "final theory", you're treating it as an approximation. As I understand it, this is the current mainstream view.

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.

No, that's not an accurate description of what happened. What happened was that, for decades, a model with a zero cosmological constant was the best fit to the data. Then we got more and better data, and a model with a nonzero cosmological constant became the best fit to the data.

A theory that changes is not precisely the same theory. Without any prediction of the value of the cosmological constant, it's not predictive in a useful sense anyway.

All during that time, cosmologists were taking measurements and using them to estimate the value of the cosmological constant. Nobody "abandoned" the concept; it was always there. But until the value "zero" was no longer within the error bars of the measurements (which happened, IIRC, sometime in the mid-1990s), nobody could say for sure whether it was actually present.

It's probably more accurate to say that some did not abandon it. Einstein announced his abandonment, probably because he knew exactly why he put it there and could no longer see any justification.

No, they aren't. They're different particular models using the same underlying theory (GR). Just as a Newtonian model of the solar system that includes only the planets, and a Newtonian model of the trajectory of a baseball in Earth's gravity, are two different particular models using the same underlying theory (Newtonian mechanics). You wouldn't say that two such Newtonian models were "different versions" of Newtonian mechanics, would you?

There is one and only one version of Newton's laws of gravity and they apply to planets and baseballs equally. We have historically two versions of GR, with and without a cosmological constant.

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?

References, please? What, exactly, is "not settled"?

I'll try to dig up some.

Asking when the cosmological constant began to dominate the universe's dynamics is very different from asking whether its value is zero or nonzero. The latter question is settled; it's nonzero.

I wasn't asking when it dominated, but rather was it there from the start? The later is probably unanswerable. There is a long way to travel to settle these questions IMO.

Do you really think cosmology is settled, wrapped up with a neat little bow? Do you read current papers much or do you rely on textbooks?

Correct. Inflation theory requires that the vacuum state of the universe during the inflationary period was very different from the vacuum state of the universe today. Today's vacuum state has a very, very small (but nonzero) cosmological constant. The inflation vacuum had (if the theory is correct) a very, very large cosmological constant. GR can model both scenarios, at least as far as the dynamics of spacetime goes, but it can't explain why the cosmological constant should take one value rather than another, or why the value should change at some point. From the standpoint of GR, the value of the constant (and whether or not it changes at some point during the universe's evolution) has to be put in "by hand", so to speak, as an input to the model.

Well, does the theory say it's a constant or not? We do know that the theory does not define it's value (although I'm not sure). Did Einstein have a value in mind that would balance gravity?

None of this poses any problem for GR, in and of itself. Whatever problems there are with inflation theory (and I'm not saying there aren't any; I am not familiar enough with the current literature in this area to assess that--and you said you were going to start a separate thread on that topic anyway, which I think is a good idea) have to do with issues that are outside the purview of GR.

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

I don't get the point of that, perhaps to enshrine GR? Einstein himself would not do that.

The only important point I would like to make is that we should not treat our theories as final, It's a lesson from history. I also think we need to be a bit more conservative in cosmology about what we claim to know. Inflation for example is commonly treated as a confirmed event without any evidence beyond "see how nicely it fixes a problem with BBT".

 

[Drakkith]

Arguing about whether a theory is right or wrong is pointless. It's almost guaranteed that future work will find places where current theories fail. If anyone's here to simply say "we could be wrong", well then you've wasted your time, as scientists already know this and take this into account every day. It's the reason we continue to test current theories and search for new ones.

 

[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.