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).