What is the meaning of expansion in Loop Quantum Cosmology?

[TrickyDicky]

Usually at first, when trying to understand what universe expansion is, one asks: what is the universe expanding into? And the answer of course is that it doesn't expand into anything, we don't need to postulate bigger universe or a higher dimension or anything like that where the volume of the universe expands into, GR doesn't work that way.

Ok, so if we have no way to say the volume of the universe is actually increasing, then the next step is to say that galaxies are just moving apart, but when one confidently asks this, the answer is usually along these lines:according to GR, there is no meaningful way to assert that remote gallaxies are moving apart because due to curvature there is no sensible way to define relative velocity at those distances, because parallel transportation in a curved manifold is path dependent. In other words it can be said with the same truth that remote galaxies are at rest wrt us, or traveling at superluminal motion from us, because their state of motion is undefined.

So at this point, it gets a little tough to understand what is meant by expansion, because if neither lengths can be said to increase in time by the above property of GR manifolds, nor volume of the universe can be said to increase because to do that one more dimension would have to be postulated for the universe to expand into something, what else do we base the notion upon?

I tried asking if it was space itself which expands or stretches, but apparently that is not the case either, because then space would have to be some kind of material stuff with that property, but according to GR such notion is forbidden.

Is "expansion of the universe" just some kind of metaphor not meant to be taken literally?

 

[Calimero]

It is often said here on this forum that GR doesn't provide unique way to define velocity on great distance. However, first law that someone intereseted in cosmology will encounter is Hubble law, v=H₀D. This can be very confusing.

In order for Hubble law to be correct, even for large distances and v>>c, one should be careful how to interpret distance and velocity. Basically, all the measurements must be made "now", or in the same proper time since the Big Bang.

 

[TrickyDicky]

It is often said here on this forum that GR doesn't provide unique way to define velocity on great distance. However, first law that someone intereseted in cosmology will encounter is Hubble law, v=H₀D.

To avoid confusions due to the problem of defining relative velocity in GR, I think the Hubble law (for large distances) is more properly written in terms of the real measured variables:

measured redshift=H₀D with distance D based on brightness by standard candles and leave v for galaxies in our vecinity where the red or blue shift clearly indicates a well defined relative velocity wrt us.

So I'm not sure the Hubble law helps clarify my points.

 

[Calimero]

So I'm not sure the Hubble law helps clarify my points.

Well it does. If you want to talk about velocities (thus expansion) at cosmic scales, you are talking about Hubble law. Question is, what are those v and D that goes into it. If you are clear how to define them or measure them, then there is no problem. Your assertion that 'according to GR there is no sensible way to define relative velocity at those distances' is not true. What is true is that according to GR there is no unique way to define velocity at great distances.

 

[marcus]

Usually at first, when trying to understand what universe expansion is, one asks: what is the universe expanding into? And the answer of course is that it doesn't expand into anything, we don't need to postulate bigger universe or a higher dimension or anything like that where the volume of the universe expands into, GR doesn't work that way.

Ok, so if we have no way to say the volume of the universe is actually increasing,...

Huh? Volume of a finite volume space can in principle be measured by observers on the inside. We can say pretty accurately how fast vol is increasing actually!

If you measure volumes the instantaneous way (imagine freezing expansion so they don't change while you try to measure them) then they increase by 0.022 percent per million years.

A given large scale volume if you could measure it, a million years later would be
1.00022 times what it was to start with.

This is based on a number which the Hubble Space Telescope was put up to measure as one of its main goals (the "Hubble Key Project" led by Wendy Freedman).

A distance (measured instantaneously) would after a million years be
1.000073 times what it was to start with.

These are measures of distance and volume that cosmologists actually USE to state this law and use a lot in doing their work---they know exactly what they mean by distance and volume and in the case of Hubble law expansion the one used is this instantaneous measure. Socalled "proper" distance at the present moment.

It is simple and intuitive. It is the distance you would measure with radar or with string and yardstick if you could freeze expansion so things wouldn't frustrate you by changing while you are in the act of measuring. Of course there are alternatives, there always are

So at this point, it gets a little tough to understand what is meant by expansion, because if neither lengths can be said to increase in time by the above property of GR manifolds, nor volume of the universe can be said to increase because to do that one more dimension would have to be postulated for the universe to expand into something, what else do we base the notion upon?

Heh heh. This makes no sense at all. We CAN say precisely about rates of distance increase (you just specify what you mean by distance and it falls out) and we CAN say rates of vol increase. We get anti-science trolls from time to time who INTENTIONALLY refuse to understand, maybe they think science threatens Genesis (I don't think it does at all!) and so they want to discredit science. Or something. I assume you are trying sincerely to understand, and are not one of those people.

You are beginning to sound a wee bit disingenuous to me. But maybe I am wrong---I often make mistakes. Maybe I have the wrong impression.
Maybe you are sincerely trying to understand. In that case I want to help. Here is what I would say you could try. Try this and see if you understand better:

A beginner in cosmo needs to connect immediately with one definite idea of distance, at first, and not be distracted by alternatives. You can learn alternatives later. You know on the surface of the Earth there are alternative measure so of distance between two points. Road distance, airplane distance, great circle distance along the surface, tunneling straight through the Earth distance. Obviously in any curved space there are alternatives and you have to define. You have to specify. Only silly people dither and tear their hair because there are several ways to measure the distance between two points on the surface of the earth.

So try this: forget about any alternatives and think only of the instantaneous distance, which is what goes into the Hubble law v = Hd. The Hubble law is very basic, it is the mathematical meaning of expansion. So it is good to have your main idea of distance be compatible with the basic law.

The present measured value of H is what I was telling you when I said that largescale distances increase to 1.000073 what they were, in a million years.
And corresponding volumes increase to 1.00022 what they were.

B. Crowell, I'd be glad if you would check me here if you have a moment. Are my numbers right or did I make a mistake with the decimal point somewhere?

It should be true that if you cube 1.000073 you get approximately 1.00022.

Also Tricky D. remember that according to the familiar commonsense meaning of MOTION, something that is moving must be getting somewhere, it must be approaching some destination, getting nearer a target. That's built into our ordinary idea. If something is not getting closer to something else it is not moving in the ordinary sense.

 

[TrickyDicky]

Huh? Volume of a finite volume space can in principle be measured by observers on the inside.

Hmm, is the volume of the universe finite, in your opinion?
On the other hand, you are not even rejecting my assertion that the universe is not expanding into anything, so there is no way to check your numbers, do you think otherwise? If so, explain.

We get anti-science trolls from time to time

So I've heard, I think they disguise as self-righteous mainstreamers

 

[TrickyDicky]

Your assertion that 'according to GR there is no sensible way to define relative velocity at those distances' is not true. What is true is that according to GR there is no unique way to define velocity at great distances.

What's the difference? If I say they are at rest and you say they are at superluminal velocity, and we are both right, how is it defined then?

 

[bcrowell]

Your assertion that 'according to GR there is no sensible way to define relative velocity at those distances' is not true. What is true is that according to GR there is no unique way to define velocity at great distances.

What's the difference? If I say they are at rest and you say they are at superluminal velocity, and we are both right, how is it defined then?

Calimero is making a valid distinction. Cosmological models come with a preferred frame of reference defined at any point in spacetime, which is the frame of an observer moving with the Hubble flow (or, alternatively, the frame in which the dipole moment of the CMB vanishes). Along with this preferred frame, we have a preferred time, which is the time on a clock that is in the preferred frame. This makes it possible, for example, to define the distance L between two galaxies at one moment in time. First we define "at one moment in time" according to the preferred time coordinate. Then we define the distance in terms of a series of rulers, each at rest relative to its own local preferred frame, at that moment in time. This L increases over time, which we can choose to interpret as meaning that space expands, or as meaning that the galaxies are in motion relative to one another.

To give an unambiguous meaning to the statement that space expands, you can use the volume expansion $\Theta$. Let the set of all points in a spacetime (or some open subset of it) be expressed as the union of geodesics. This is referred to as a foliation in geodesics, or a congruence. Let the four-velocity vector tangent to such a curve be $u^a$. Then we define $\Theta=\nabla_a u^a$. This is exactly analogous to the classical notion of the divergence of the velocity field of a fluid, which is a measure of compression or expansion. Since $\Theta$ is a scalar, it is coordinate-independent. Negative values of $\Theta$ indicate that the geodesics are converging, so that volumes of space shrink. Positive values say that volumes of space expand.

 

[bcrowell]

B. Crowell, I'd be glad if you would check me here if you have a moment. Are my numbers right or did I make a mistake with the decimal point somewhere?

Your numbers seem to me to be the right order of magnitude. I'm not confident of being able to get factors of 2 and pi right off the top of my head. I think basically your expansion factor of 1.000073 in a million years is something like $1+k\Theta (10^6\ \text{years})$, where $\Theta$ is the volume expansion I defined in #8, and k is some unitless constant of order unity that it would take me an afternoon to convince myself I had right. I think that $\Theta$ is basically the Hubble constant in the case of a cosmological solution (again, with possible pesky unitless factors of order unity).

[EDIT] Comparing this paper http://arxiv.org/abs/gr-qc/0010076 and this WP article http://en.wikipedia.org/wiki/Hubble_law#Redshift_velocity_and_recessional_velocity side by side, I think for small distances, the Hubble constant equals $\Theta/3$. Again for small distances, the fractional rate of change of the scale factor is the same as the Hubble constant, so for the linear expansion per million years, I get 1+7.4*10^-6, which disagrees by a factor of 10 compared to what you had. My calculation was 1 pc = 30.857 10^16 m, H=(72 km/s)/(10^6 pc), H*(1000000*365.25*24*3600)=7.4*10^-6.

 

[TrickyDicky]

Calimero is making a valid distinction. Cosmological models come with a preferred frame of reference defined at any point in spacetime, which is the frame of an observer moving with the Hubble flow (or, alternatively, the frame in which the dipole moment of the CMB vanishes). Along with this preferred frame, we have a preferred time, which is the time on a clock that is in the preferred frame. This makes it possible, for example, to define the distance L between two galaxies at one moment in time. First we define "at one moment in time" according to the preferred time coordinate. Then we define the distance in terms of a series of rulers, each at rest relative to its own local preferred frame, at that moment in time. This L increases over time, which we can choose to interpret as meaning that space expands, or as meaning that the galaxies are in motion relative to one another.

To give an unambiguous meaning to the statement that space expands, you can use the volume expansion $\Theta$. Let the set of all points in a spacetime (or some open subset of it) be expressed as the union of geodesics. This is referred to as a foliation in geodesics, or a congruence. Let the four-velocity vector tangent to such a curve be $u^a$. Then we define $\Theta=\nabla_a u^a$. This is exactly analogous to the classical notion of the divergence of the velocity field of a fluid, which is a measure of compression or expansion. Since $\Theta$ is a scalar, it is coordinate-independent. Negative values of $\Theta$ indicate that the geodesics are converging, so that volumes of space shrink. Positive values say that volumes of space expand.

This is fine, only you are still assuming without rigour that L increases over time (so what happens when one uses coordinates that allow remote galaxies to be at rest wrt us) and that the four-velocity vector $u^a$ is defined in a unique way at big distances, even though as you know this is not warranted according to GR.

 

[bcrowell]

This is fine, only you are still assuming without rigour that L increases over time (so what happens when one uses coordinates that allow remote galaxies to be at rest wrt us) and that the four-velocity vector $u^a$ is defined in a unique way at big distances, even though as you know this is not warranted according to GR.

L is defined in a coordinate-independent way. The four-velocity vector $u^a$ need not be defined in a unique way, because $\Theta$ is a scalar and therefore coordinate-independent, so $\Theta$ is uniquely defined (given the foliation) regardless of any ambiguity in u. (Also, u is just a coordinate velocity. It is not interpreted as the velocity of one galaxy relative to another.)

 

[TrickyDicky]

L is defined in a coordinate-independent way. The four-velocity vector $u^a$ need not be defined in a unique way, because $\Theta$ is a scalar and therefore coordinate-independent, so $\Theta$ is uniquely defined (given the foliation) regardless of any ambiguity in u. (Also, u is just a coordinate velocity. It is not interpreted as the velocity of one galaxy relative to another.)

You forgot to add an ingredient that has nothing to do with GR itself, namely what allows us to use the fluid description, with an average motion of matter at each point (average 4-velocity $u^a$ from which the divergence $\Theta$ is defined): the homogeneous distribution of matter expectation.
Other than that, thanks for a satisfactory answer.

 

[marcus]

Looking back to post #9 it seems there could be some misunderstanding about the rates of proper distance and volume increase, so I had better explain my reasoning earlier. Here is what I was saying.

...

If you measure volumes the instantaneous way (imagine freezing expansion so they don't change while you try to measure them) then they increase by 0.022 percent per million years.

A given large scale volume if you could measure it, a million years later would be
1.00022 times what it was to start with.

A distance (measured instantaneously) would after a million years be
1.000073 times what it was to start with.
...
...
The present measured value of H is what I was telling you when I said that largescale distances increase to 1.000073 what they were, in a million years.
And corresponding volumes increase to 1.00022 what they were.

B. Crowell, I'd be glad if you would check me here if you have a moment. Are my numbers right or did I make a mistake with the decimal point somewhere?

It should be true that if you cube 1.000073 you get approximately 1.00022.

Here is the reasoning. Assume the Hubble rate is 71 km/s per Mpc so (temporarily including spurious precision) we have the Hubble distance is
13770 million light years.

Now the Hubble distance is increasing at rate c, so in a million years a distance of 13770 million lightyears will essentially increase by one million lightyears. I'll neglect minuscule corrections in the umpteenth decimal place.
It will essentially then be 13771 million lightyears, which is
(1 + 1/13770) times what it was at the start.

This factor applies to all largescale distances according to Hubble Law (distances defined in the way appropriate to the law).

So any largescale distance, after a million years, is 1 + 1/13770 times what it was at the start. And that is 1.00073

To get the corresponding number for volume, you just CUBE this ratio:

(1 + 1/13770)³ = 1.00022.

 

[bcrowell]

Hi, marcus,

The reason for the discrepancy between our results was that I mistakenly used 1 pc = 30.857 10^16 m. It's actually 30.857 10^15 m. Fixing that, I now confirm your result.

Ben

 

[bcrowell]

You forgot to add an ingredient that has nothing to do with GR itself, namely what allows us to use the fluid description, with an average motion of matter at each point (average 4-velocity $u^a$ from which the divergence $\Theta$ is defined): the homogeneous distribution of matter expectation.
Other than that, thanks for a satisfactory answer.

No, I didn't forget such an ingredient, and the existence of such a four-velocity does not have anything to do with the assumption of a homogeneous distribution of matter. Actual CMB measurements reveal the universe to be not completely homogeneous, but one can still define a preferred frame based on the local Hubble flow. It is certainly a nontrivial assumption that such a local rest frame exists and is unique -- such a frame is not something you can define for any randomly chosen spacetime -- but homogeneity isn't required. I think the necessary assumption may be that it's a perfect fluid.

 

[apeiron]

I tried asking if it was space itself which expands or stretches, but apparently that is not the case either, because then space would have to be some kind of material stuff with that property, but according to GR such notion is forbidden.

I think the replies have so far failed to focus on your option 3.

Now GR is just a model. And just because it does not model reality in some ways does not forbid those aspects from actually existing (although it does heavily constrain them, of course).

So GR famously did away with the need for an ether as a material to carry the waves of EM or other forces. But the idea of the vacuum as some kind of substance - as something to be modeled in material terms - is one that people still keep coming back to.

For example, there is Frank Wilczek's book, The Lightness of Being, where he argues for a model of the vacuum as a condensate.

And also of course, we know that spacetime is both expanding and cooling. There is an actual thinning energy density, a thermal gradient. It was the existence of hot matter fields that gave kinetic direction to the expansion. So there is a material stuff that is expanding, not just an empty set of dimensions.

If GR only sees "expansion" but not "cooling", then clearly the answer is not that GR forbids a "stuff" based ontology, just that it is incomplete as a model in that regard.

 

[marcus]

Hi, marcus,

The reason for the discrepancy between our results was that I mistakenly used 1 pc = 30.857 10^16 m. It's actually 30.857 10^15 m. Fixing that, I now confirm your result.

Ben

Thanks!

Ben, you might be interested in parts of this new paper
http://arxiv.org/abs/1103.2475
particularly equation 2.4 and the mention right after eqn 2.12 of the 'bounce surface'

this is the spacelike hypersurface where the Hubble parameter stops being negative and becomes positive. Where H(t) = 0
It initiates a brief period of superinflation. Where H plateaus at a high value--actually almost Planck frequency level, reciprocal of Planck time.

General relativity lacks a canonical "time slice" like that. But the last scattering era of the CMB gives us an approximate "instant" which is useful. This feature of bounce cosmology in as sense "parallels" that.

I recall discussing some of this with Apeiron. The bounce cosmo model also has a maximum value of H(t) achieved soon afterwards. It marks the end of superinflation and the onset of ordinary inflation (if an inflaton is present).

The paper I was reading with Apeiron is a good introduction
http://arxiv.org/abs/1005.5491
but it does not have some of this interesting technical detail about a canonical timeslice and the contribution of the superinflation episode to a long slow-roll ordinary inflation (assuming the presence of an inflaton).

The superinflation episode comes free (in bounce cosmo) without any exotic hardware or finetuning, but is not adequate by itself so an inflaton with the usual sort of potential is still required.

 

[TrickyDicky]

No, I didn't forget such an ingredient, and the existence of such a four-velocity does not have anything to do with the assumption of a homogeneous distribution of matter. Actual CMB measurements reveal the universe to be not completely homogeneous, but one can still define a preferred frame based on the local Hubble flow. It is certainly a nontrivial assumption that such a local rest frame exists and is unique -- such a frame is not something you can define for any randomly chosen spacetime -- but homogeneity isn't required. I think the necessary assumption may be that it's a perfect fluid.

You are conflating here two concepts, the Weyl postulate and spatial homogeneity, the former is what gives us the possibility of choosing that preferred frame and have a "cosmic time" and as you say has nothing to do with homogeneity, but it has nothing to do with expansion either, as shows the fact that you can build models with this postulate that are static, just two name two that are also homogeneous: one is the trivial empty Minkowski spacetime and the other the Einstein Universe which is unstable and needs the cosmological term, but they could be inhomogeneous too. Another model such as de Sitter's is compatible with expansion but doesn't fulfill the Weyl's postulate.
The fact that at least a static matter dominated model(Einstein's) can be built that is also spatially homogeneous, would seem to mean, according to my reasoning that homogeneity is not related to expansion, but in this case staticity is a previous requirement on the metric by demanding all the components to be functions of r only (all time derivatives vanish), and the cosmological term must never vanish. Had Einstein not demanded this of the metric he could have been the first to find the scale factor and thus expansion.
So of course homogeneity is not a sufficient and necessary conditon for a universe to expand (see for instance Tolman-bondi model), that is not my point, rather in the specific case of the RW metric expansion enters thru the scale factor in the space part of the metric, that is a condition of spatial homogeneity, not thru the preferred frame postulate of the time part.

The existence of a four-velocity is not related to homogeneity, the existence of a mean four-velocity in the universe is.

A perfect fluid has isotropic pressure but there seems to exist inhomogeneous perfect fluids, so I'd say a perfect fluid assumption is not enough. You need to explicitly assure spatial homogeneity, isotropy alone is not enough, as there are isotropic models that are static.

 

[marcus]

Tricky, I see you asked me questions in this earlier post. I will try to respond.

Hmm, is the volume of the universe finite, in your opinion?
On the other hand, you are not even rejecting my assertion that the universe is not expanding into anything, so there is no way to check your numbers, do you think otherwise? If so, explain.

I have no opinion on whether spatial finite or infinite. Data is consistent with either---just say "nearly flat" in any case. WMAP confidence interval for Omega-sub-k etc. etc.

I have often asserted that according to the usual cosmo model the universe is not expanding into anything. I make that as a kind of routine assumption, though I would not be able to prove the standard model is right, on that score.

I don't understand why I should want to reject your assertion since I make the same assertion myself.

My numbers were just a statement of Hubble Law. Regarding largescale distances and volumes. Hubble Law is well checked, so I think my numbers are. They are trivially equivalent to saying 71 km/s per Mpc.

I didn't understand your post early in this thread where I thought you were a layman overdramatizing and protesting the conceptual difficulty of expansion. I didn't realize that you have a lot of expertise to offer. Sorry.

I recently looked at some of your other posts in the Relativity forum. I liked what I saw.
I particularly like the ether or absolute rest frame message you seem to be putting out.
For example:

Roineust, I think it is important to understand that every law, every postulate in science has a certain scope of application, SR is no exception. You are asking of it something it was not meant to solve, Einstein himself repeatedly said that all SR had to say about the ether is that it was an unnecesary (superfluous) assumption in the range where SR applies, which is an idealized space (minkowskian) where masses can be neglected and all frames are inertial in the Newtonian sense (uniform velocity). This is obviouly a mathematical idealization that is not our real universe but that happens to work very well for problems where one doesn't have to take into account gravitation , which are quite a lot (all EM applications,weak force, etc ...) because the gravitational interaction is very small to be detected by our experiments , like in the particle accelerator experiments you cite (it is within experimental error bars).
If you want to take those gravitational effects into account you have to turn to GR, there you will find that in practical terms an ether is used (even though you can't use the taboo word ether, it is frowned upon due to historical connotations). An absolute rest frame is considered for a certain set of "fundamental observers". This absolute rest frame is realized for instance in the form of the CMB that fills the vacuum. Of course you'll be told that it is not a "real" absolute rest frame but in practical terms is used as if it were because otherwise we can't concoct a coherent cosmic time line, or in other words the absolute clock you seek is been around for decades, is the one that counts the time from the BB to now.

I have often emphasized the practical existence of cosmic time, or Friedmann model time, or CMB rest frame time here in Cosmo forum. It is really important pedagogically for beginners to get the idea of a family of what you call "fundamental" observers, at rest relative to the ancient light, and the absolute clock implied, so that one can discuss cosmo issues meaningfully without a lot of fuss and bother. Everything one wants to say is much easier when one has a family of observers at rest.

So I like the message you seem to have been getting across.

I do want to point out that the new Ashtekar Sloan paper has another support for the practical reality of a natural "universe time".
http://arxiv.org/abs/1103.2475

You get a natural "universe time" in quantum cosmology as a bonus for resolving the singularity into a bounce. It is the keystone in Ashtekar's discussion of the main topic of the paper which is "The Probability of Inflation".

So moving from classical to quantum cosmology makes your case appear stronger.

 

[TrickyDicky]

Marcus, your kind words are undeserved but thanks anyway.
The OP was meant to reinforce my view of certain concepts by the always healthy procedure in science of never taking anything for granted, not even the basics. It may seem a convoluted way but it works for me, even if it is often misinterpreted.

 

[marcus]

So have you encountered much opposition when you assert your main thesis? If I understand you correctly, it is that (at least if you put matter in) GR has some kind of natural "unverse time".

Maybe we should distinguish pure GR from cosmology. It is cosmology that has a universe time. It becomes a question of nuance: how publicly one should take it as serious. Or how seriously one should take it in public. :-D
=====================

I'll mention an interesting thing about QG. At very high densities quantum effects dominate and gravity becomes repellent, so the distribution of matter tends toward uniformity.
So a certain degree of homog + isotropy is the natural result of a bounce.

I keep thinking that rather than postulating it one should be able to prove the Hermann Weyl postulate. (Under certain assumptions.)

 

[TrickyDicky]

So have you encountered much opposition when you assert your main thesis? If I understand you correctly, it is that (at least if you put matter in) GR has some kind of natural "unverse time".

Maybe we should distinguish pure GR from cosmology. It is cosmology that has a universe time. It becomes a question of nuance: how publicly one should take it as serious. Or how seriously one should take it in public. :-D
=====================

I'll mention an interesting thing about QG. At very high densities quantum effects dominate and gravity becomes repellent, so the distribution of matter tends toward uniformity.
So a certain degree of homog + isotropy is the natural result of a bounce.

I keep thinking that rather than postulating it one should be able to prove the Hermann Weyl postulate. (Unde2r certain assumptions.)

Yes, it has to be added as postulate to the GR equations, as you know the equations by themselves have many unphysical solutions so one must constrain them by adding sensible assumptions such as existence of fundamental observers, isotropy... with the rule that we should use the minimum number of constraints compatible with observations (Occam).
It was already implicit in Einstein 1917 first model of the universe, even before Weyl formalized it in 1923. The congruence of timelike worldlines seems like a very natural assumption and is only fortunate that posterior seminal findings like the CMBR are useful to embody the idealized fundamental observers. Unfortunately, other than checking its compatibilty with the observed universe, there is no way that I know to "prove" it.

 

[marcus]

Unfortunately, other than checking its compatibilty with the observed universe, there is no way that I know to "prove" it.

I didn't mean prove it in the context of GR. I meant from QC (have a look at the Ashtekar Sloan paper (my crutch for remembering it is 2475 of March = 1103.2475). They essentially do that, see pages 7 and 12.

Sure you can be skeptical about QC but a number of people are beginning to see it as testable and interesting for various reasons. There's been a big gain in cred and visibility in the past 3 or 4 years.

In plain GR you cannot state initial conditions at the singularity because...well...it is a singularity. In quantum cosmology you can state initial conditions at the start of expansion because it is a bounce. There is a hypersurface where the Hubble rate H = 0.

 

[Farahday]

If the universe is expanding then by definition there must be more now than there was before. This implies the universe must be finite. If that is the case, then for every point within it there must exist another point within a finite distance at which motion in any direction will not increase the distance between them (pretty simple stuff). I see no evidence of such a point.

 

[marcus]

If the universe is expanding then by definition there must be more now than there was before. This implies the universe must be finite...

Please be sure you have read and understood this SciAm article
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
called Misconceptions about the Big Bang, by Lineweaver and Davis.

There should be an FAQ somewhere that explains why the U can be infinite volume even though distances within it are expanding. It's funny you would not get that, but maybe it is explained somewhere.

I'll check the Ned Wright FAQ and see if he explains it.
Well this is the closest I think he comes in his FAQ.
http://www.astro.ucla.edu/~wright/infpoint.html
He is focusing on a different issue but at least he describes an infinite expanding universe and has some pictures. The rest of the FAQ is here:
http://www.astro.ucla.edu/~wright/cosmology_faq.html

Cosmo is a mathematical science, which means when you hear some words you have to figure out what they really mean in terms of the model. You can't just make a naive verbal translation. Here "expanding universe" means largescale distances within it are increasing according to a certain definite pattern. It does not necessarily mean that overall volume is increasing because the vol may be infinite, and therefore not defined.

In Cosmo you don't go merely by the words (literally, in a contextual vacuum). Go by what the words are trying to say in the context of the mathematical model. Go by what the words are trying to tell you about the model. If you need help, ask questions.

Please read the Lineweaver Davis article before you post further about cosmology. It will save you a lot of trouble and bother to get past the basics. Good luck!

 

[TrickyDicky]

I didn't mean prove it in the context of GR. I meant from QC (have a look at the Ashtekar Sloan paper (my crutch for remembering it is 2475 of March = 1103.2475). They essentially do that, see pages 7 and 12.

Sure you can be skeptical about QC but a number of people are beginning to see it as testable and interesting for various reasons. There's been a big gain in cred and visibility in the past 3 or 4 years.

In plain GR you cannot state initial conditions at the singularity because...well...it is a singularity. In quantum cosmology you can state initial conditions at the start of expansion because it is a bounce. There is a hypersurface where the Hubble rate H = 0.

I'm afraid my shallow knowledge about QC prevents me from any productive contribution.
But after reading those pages you link I get the impression that indeed is hard to reconcile the FRW cosmology singularity with the bounce surface of QC. And I see no way out of this as long as the initial singularity remains there. Of course I think that seems to be the main purpose of QG, to deal scientifically with the singularity.
Maybe one could think that by the "universal time" of the fundamental observers one could try to derive a preferred Ho, but that is not feasible in FRW models, precisely due to the fact that the Hubble flow depends on the particular matter distribution in every region and only is supposed to reach a stable magnitude at very large scales and surely can never be zero.
But as I said this is not a difficlty that has to do properly with GR, but with GR+ certain boundary conditions or assumptions, in this case, the standard ones.

 

[Farahday]

Please be sure you have read and understood this SciAm article
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
called Misconceptions about the Big Bang, by Lineweaver and Davis.

There should be an FAQ somewhere that explains why the U can be infinite volume even though distances within it are expanding. It's funny you would not get that, but maybe it is explained somewhere.

I'll check the Ned Wright FAQ and see if he explains it.
Well this is the closest I think he comes in his FAQ.
http://www.astro.ucla.edu/~wright/infpoint.html
He is focusing on a different issue but at least he describes an infinite expanding universe and has some pictures.

He makes the critical distinction between the OBSERVABLE universe - which is finite - and the entire universe. How is it that space between mass bearing bodies knows how to inflate while space within mass bearing bodies seems to lack that capability?

The rest of the FAQ is here:
http://www.astro.ucla.edu/~wright/cosmology_faq.html

Cosmo is a mathematical science, which means when you hear some words you have to figure out what they really mean in terms of the model. You can't just make a naive verbal translation. Here "expanding universe" means largescale distances within it are increasing according to a certain definite pattern. It does not necessarily mean that overall volume is increasing because the vol may be infinite, and therefore not defined.

So do you contend the observable universe is inflating into the entire universe - or that the entire universe is inflating and is sucking celestial bodies along with it?

 

[TrickyDicky]

If the universe is expanding then by definition there must be more now than there was before. This implies the universe must be finite. If that is the case, then for every point within it there must exist another point within a finite distance at which motion in any direction will not increase the distance between them (pretty simple stuff). I see no evidence of such a point.

A very valid point (no pun intended). This is easy to see in the balloon analogy.

 

[Farahday]

A very valid point (no pun intended). This is easy to see in the balloon analogy.

On a balloon you will eventually reach a point such that motion in any direction will not increase the distance - in fact distance will DEcrease.

 

[marcus]

... I get the impression that indeed is hard to reconcile the FRW cosmology singularity with the bounce surface of QC. And I see no way out of this as long as the initial singularity remains there. Of course I think that seems to be the main purpose of QG, to deal scientifically with the singularity...

One of the main purposes of QC is, indeed, to cure the singularity in a scientific (that is, in an empirically falsifiable if you will) way. One wants a model of the universe that does not break down at the start of expansion, and one wants it to be empirically testable.

This is an active field involving several different theoretical approaches. Here are the keyword "quantum cosmology" papers that appeared 2008-present, ranked by cites:
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=dk+quantum+cosmology+and+date+%3E+2007&FORMAT=WWW&SEQUENCE=citecount%28d%29

The search finds 320 QC papers. Glancing at the first 50 one sees that they are mostly bounce-type. And the second-most-cited is a review of bounce cosmologies. That is probably the most active area within QC. (Also getting the most attention from phenomenologists look for ways to test observationally.)

In bounce cosmology H is initially negative, in the collapse phase, and subsequently it is positive, when expansion starts. So intuitively it must cross zero.
And that is what happens in LQC, as you see in Ashtekar's paper: at the moment of the bounce the Hubble rate H = 0.

In LQC they work out a quantum corrected version of the Friedmann equation which you can see on page 5. It is equation (2.4). I assume you would have noticed that.

The quantum corrections to FRW model take effect only at very high density. And at very high density gravity behaves as a repellent force. You can see that in (2.4).
The density at bounce is calculated to be a substantial fraction of Planck density.
(See the sentence immediately following equation (2.4) which gives it's value.)