Max. rate of expansion of space?

[coyote2]

Since I see the Big Bang was the beginning of space; if space is infinite, does that mean that space can expand at an infinite rate?

(Thanks in advance from this layman; I've started Brian Greene's "Hidden Reality" and despite laymen being it's target audience, I'm stuck on this question.)

 

[marcus]

You have to be careful with popularizations. Many are written to make money, to sell to wide audience, rather than to honestly present the state of scientific observation and conjecture.

Most working cosmologists do not accept or use "multiverse" models. (Yet Greene's book is largely about "multiverse" speculation.)

So far there is no scientific reason to favor infinite over finite space. Both versions of the standard cosmo model may be used in the same paper. So far they fit the data about equally well, so it is an open question. Keep both possibilities in mind, is the idea.

(If space is infinite now, then it always was. And expansion started from infinite volume.)

So far there is no scientific reason to suppose that space and time "began" with the start of expansion or any other known event. There are models which do not go back further than the start of expansion, and there are models which do go back further in time. And both fit the data equally well.

As more and better data accumulate we will be better able to distinguish and see which models fit best. There is actually some progress being made in this currently! It's exciting, but it's not over yet.

 

[marcus]

You asked about expansion rate. What is the max?

This is mind-stretching. The current expansion rate (as a percentage growth in distance per million years) is pretty much unimaginably slow. The early expansion rate (as percentage growth in distance per billionth of a second) is pretty much unimaginably rapid--according to prevailing estimates.

It's tough. The two rates almost do not fit on the same scale.

I don't want to risk a big stretch (you just got here) so I will not say much about the early universe rate. I'll just tell you what we currently measure to be the expansion rate NOW. It is very slow.

Distances in the universe (large scale and on average) are currently increasing at the rate of 1/140 of one percent every million years.

That is a way of expressing a quantity called the "Hubble parameter" in ordinary familiar units.

In the early universe, the Hubble parameter was vastly more rapid. One could say indecently and preposterously more rapid. We can't do anything about this. The best mathematical models, based on a law of gravity whose detailed predictions have been meticulolusly checked in the situations where we know how to check, tell us this.

We are talking about a difference like between 10^-18 per second and 10⁴³ per second. If your taste lies in the direction of such extreme numbers, keep on asking and I or somebody else can supply more detail about models of the early universe, and links to the actual research literature (not Brian Greene )

 

[coyote2]

Thank you very much for your wonderful replies, marcus.

I do understand that Green's book is largely speculative (and simplified), and I'm simply seeking a grasp of the bases of that speculation.

(Speaking of "speculation", I guess I'm interested in it because it seems to me that quantum mechanics seems strange enough, that an encompassing theory might well be rather surprising.)

(If space is infinite now, then it always was. And expansion started from infinite volume.)

Gulp. Is there a way I might understand how "infinite volume" could expand?


Are the vast differences between current and past expansion percentage rates simply proportional to the distances involved?

 

[WannabeNewton]

Are the vast differences between current and past expansion percentage rates simply proportional to the distances involved?

If you are talking about the expansion of space itself then it is a function of time and is usually a power law.

 

[bapowell]

Gulp. Is there a way I might understand how "infinite volume" could expand?

Sure (but take a breath first). Imagine a rubber sheet with grid marks painted on it stretching out infinitely far in all directions from your position. Now imagine that the rubber sheet is stretched out isotropically from your vantage point. The grid marks will grow in size, charting the expansion of the rubber sheet. This is how an infinite volume undergoes expansion. The big bang in this case is the moment at which this expansion began.

 

[bapowell]

Are the vast differences between current and past expansion percentage rates simply proportional to the distances involved?

There are two things at play here: the expansion rate of the universe -- the rate at which the grid marks on the rubber sheet grow, and the speed at which distant objects attached to this sheet appear to recede from Earth. In a homogeneous universe, the rate of expansion is the same at all points in the universe, and is given by the Hubble parameter, $H$. (Really, it's determined by the rate of the change of the scale factor, $a(t)$, which governs how meter sticks grow in time. In terms of the scale factor, the Hubble parameter is $H=\dot{a}(t)/a(t)$, where $\dot{a}(t)$ is the time derivative of $a(t)$.) Now, the speed at which distant objects recede from Earth depends on how far away that object is. This speed, $v$ is given by Hubble's Law:
$$v = Hr$$
where $r$ is the distance to the object. So for a given, fixed rate of expansion (set by $H$), we find that objects recede from us at a speed that is proportional to their distance from us.

So to finally answer your question, in the real universe, the Hubble parameter is generally a function of time, and so the rate of expansion of the universe varies with time, but not location in a homogeneous universe.

 

[coyote2]

Sure (but take a breath first). Imagine a rubber sheet with grid marks painted on it stretching out infinitely far in all directions from your position. Now imagine that the rubber sheet is stretched out isotropically from your vantage point. The grid marks will grow in size, charting the expansion of the rubber sheet. This is how an infinite volume undergoes expansion. The big bang in this case is the moment at which this expansion began.

Thank you bapowell, I may have a shot at understanding this.

Since this example uses a two-dimensional object (the rubber sheet) to stand for (three-dimensional) volume, does that mean that it's spatial expansion involves a dimension beyond three?

 

[coyote2]

There are two things at play here: the expansion rate of the universe -- the rate at which the grid marks on the rubber sheet grow, and the speed at which distant objects attached to this sheet appear to recede from Earth. In a homogeneous universe, the rate of expansion is the same at all points in the universe, and is given by the Hubble parameter, $H$. (Really, it's determined by the rate of the change of the scale factor, $a(t)$, which governs how meter sticks grow in time. In terms of the scale factor, the Hubble parameter is $H=\dot{a}(t)/a(t)$, where $\dot{a}(t)$ is the time derivative of $a(t)$.) Now, the speed at which distant objects recede from Earth depends on how far away that object is. This speed, $v$ is given by Hubble's Law:
$$v = Hr$$
where $r$ is the distance to the object. So for a given, fixed rate of expansion (set by $H$), we find that objects recede from us at a speed that is proportional to their distance from us.

So to finally answer your question, in the real universe, the Hubble parameter is generally a function of time, and so the rate of expansion of the universe varies with time, but not location in a homogeneous universe.

First, as soon as I read WannabeNewton's reply, I realized my ambition was really just to know if despite the vastly different percentage rate of spatial expansion, the distance of the expansion was constant. After I googled "Power Law" I think I understood the answer was "no".

Had I stuck with my plan to take more math and major in physics decades ago, I'd have had a much better shot at fully grasping bapowell's reply (my fault, thank you bapowell)!

 

[bapowell]

Since this example uses a two-dimensional object (the rubber sheet) to stand for (three-dimensional) volume, does that mean that it's spatial expansion involves a dimension beyond three?

No, it's just lower-dimensional for ease of explanation. To get our universe, you just have a 3D volume undergoing expansion in the same manner.

 

[bapowell]

Had I stuck with my plan to take more math and major in physics decades ago, I'd have had a much better shot at fully grasping bapowell's reply (my fault, thank you bapowell)!

Don't give up! It's difficult sometimes to gauge the level of people on the forums -- I apologize if I spoke passed you or used terms/concepts with which you are not familiar. Feel free to ask for clarification!

 

[coyote2]

No, it's just lower-dimensional for ease of explanation. To get our universe, you just have a 3D volume undergoing expansion in the same manner.

Thank you bapowell. I'm afraid I'm not quite there yet...

Perhaps my problem is that, in terms of area, "3D volume" and "space" seem equivalent to me. Which leaves me still wondering how "infinite volume" could expand. I'm sure it's just my limited imagination, I don't see how an infinite amount of volume can increase.

Or maybe my problem is I don't understand "infinite". (In two dimensions, I think of "infinite" length as going on forever, endlessly. Such that infinity + 1 = infinity.)

I promise if I can't get it this time, I'll stop wasting your time!

 

[Chalnoth]

Since I see the Big Bang was the beginning of space; if space is infinite, does that mean that space can expand at an infinite rate?

Well, there isn't any known fundamental limit to the expansion rate, however an infinite expansion rate would require infinite energy density. And that can't happen.

 

[Chronos]

The observable universe is temporally finite [~13.7 billion years] and contains a finite quantity of baryonic, non-baryonic, spatial and energy components. It is hard enough to wrap your head around that without introducing indeterminate quantities of unobservable and exotic components.

 

[coyote2]

Perhaps my problem is that, in terms of area, "3D volume" and "space" seem equivalent to me. Which leaves me still wondering how "infinite volume" could expand.

I think I get it now. I thought "volume" here meant an "http://dictionary.reference.com/browse/volume" ").

I apologize, I guess I needed to take more deep breaths. I hope there aren't too many like me who stumble in here needing clues, overwhelmed from reading pop physics.

 

[bapowell]

Right. Don't think about expansion as some region necessarily increasing in volume (in a finite universe, this would indeed be the correct view). Instead, just think of expansion as the increase in size of the grid marks you paint throughout your volume. In general relativity, this is precisely the way expansion works -- as an increase in distance between points drawn on the grid.

 

[coyote2]

Thank you bapowell. I'm afraid I'm not quite there yet...

Perhaps my problem is that, in terms of area, "3D volume" and "space" seem equivalent to me. Which leaves me still wondering how "infinite volume" could expand. I'm sure it's just my limited imagination, I don't see how an infinite amount of volume can increase.

Or maybe my problem is I don't understand "infinite". (In two dimensions, I think of "infinite" length as going on forever, endlessly. Such that infinity + 1 = infinity.)

I promise if I can't get it this time, I'll stop wasting your time!

Right. Don't think about expansion as some region necessarily increasing in volume (in a finite universe, this would indeed be the correct view). Instead, just think of expansion as the increase in size of the grid marks you paint throughout your volume. In general relativity, this is precisely the way expansion works -- as an increase in distance between points drawn on the grid.

Thank you bapowell, this reply plus time pondering helped me imagine it better at all scales.

I'd heard about (but not understood) the http://en.wikipedia.org/wiki/Big_Rip" ; it didn't occur to me that expansion was a factor at very small scales.

I see that "http://en.wikipedia.org/wiki/Timeline_of_the_Big_Bang" ").

Knowing that electromagnetic forces now keep atom nuclei from being torn apart leaves me still wondering: that means the atoms aren't expanding at all yet, right? (I'm guessing that based upon atomic particles having quantum states.)

I shudder to think how far off the rails I might be here.

 

[bapowell]

I shudder to think how far off the rails I might be here.

No, you've got it right. Bound structures -- like atoms, planets, and even galaxies -- are not expanding along with the universe. However, as you say, if the dark energy density is increasing at a sufficiently high rate, then eventually even bound structures will 'feel' the expansion.