Superluminal Recession & Cosmological Redshift

1. Jul 23, 2008

jonmtkisco

I'm taking the liberty of revising and restating this topic which started in a separate thread. Comments are welcome.

A lively debate is underway today by mainstream cosmologists as to whether the expansion of the universe implies that empty space between galaxies is also expanding. When faced directly with the question, most cosmologists will say that galaxies are moving apart because they were previously moving apart, but decline to state flatly that space itself expands. And yet it has been customary for textbooks and technical literature to explain both superluminal recession and cosmological redshift only as the result of space itself expanding. What seems clear is that the observational predictions of GR must be precisely identical regardless of whether space itself expands. Therefore, at a minimum we need a comprehensive theoretical description of both superluminal recession and cosmological redshift that does not resort to the concept of expanding space. Here are some thoughts on that subject.

Accurate application of Special Relativity depends on having a global inertial reference frame, which may be arbitrarily selected, but which cannot be accelerating, and by the same token cannot include significant gravitational objects. On the other hand, our universe appears to be homogeneously filled with gravitating matter. This means that instead of one global reference frame, we have an infinite series of tightly packed local reference frames.

Superluminal Recession

In our gravitation-filled universe, the rule of SR that no object can exceed the speed of light, c, relative to any other object, simply doesn’t apply. Objects at rest in any two local reference frames which are in motion relative to each other may have a relative velocity exceeding c. This is true even if the two frames are immediately adjacent to each other.

One might be tempted to call this is a "license to steal", in the sense that the SR speed limit of c doesn't seem to apply hardly anywhere in our universe. But the reality isn't that dire. The degree by which the velocity of an object in a local frame can exceed c relative to any other local frame is dictated entirely by General Relativity’s applicable metric of gravity. If the gravitational density is low, the degree of "violation of the speed limit" in nearby frames is infinitesimal. If the gravitational density is high, this speed limit can be "violated" to a larger degree. Even a low gravitational density enables large violations of the speed limit if the objects are extremely distant from each other, currently in the range of z=1.6.

Consider our very early observable universe, a fraction of a second after inflation is theorized to have ended, which could be visualized as being the total size of a beachball. The FLRW metric (to the extent its equation of state doesn't require modification on account of the then-dominant quark-gluon plasma) calculates that matter particles located just millimeters away from each other were receding from each other at velocities many times faster than c. This demonstrates that a tiny distance between distinct local frames is no inhibitor to observing a massive "violation" of the SR speed limit. All that’s needed is truly astounding gravitational density -- which is what theory calculates for our very early universe.

Note that any pair of particles which are observed to have a given relative recession velocity now haven’t gained relative velocity over time as their mutual distance increased. On the contrary, their relative recession velocity was enormously higher in the very early universe. In early times, the self-gravity of the universe hugely decelerated every galaxy pair's mutual recession rate; in late times, dark energy has reaccelerated them but to a much lesser degree. Absent the competing effects of those two accelerations, each pair of particles would retain the same relative recessionary momentum they had in the very early universe.

One must confront the question whether superluminal recession is a “physically real” phenomenon or just an observational artifact. If it is physically real, then it will continue regardless of how low the cosmic gravity density declines in the far future. Consider a model universe with dark energy [edit: Lambda=0 doesn't work well here]. As time passes, the gravitational density declines, and in the limit will approach zero (except for the gravity of the dark energy itself, which is more than offset by its antigravity negative pressure effect). By then superluminally receding particles (which are, say, at z=3 today) will be many times further apart. Yet this clearly begs the question, when gravitational density drops to zero in a given large but finite region, as it eventually must, how can superluminal relative recession velocities remain possible from one end of that region to the other, regardless of how widely separated the two particles are? Within its bounds, that region has in fact become converted to a true SR-compliant global frame. This logic suggests the theoretical possibility that superluminal recession is not physically real and might be an observational artifact.

If superluminal recession is merely an observational artifact, then the explanation must lie in the cosmological redshift that occurs as photons emitted by the receding particle (or galaxy) transition from each local gravitational frame to the next such frame along their path (keeping in mind that local frames are confined to an infinitesimal point and lack discrete boundaries.)

Cosmological Redshift

In order to explain cosmological redshift without resorting to the expansion of space itself, the only tools left in our kitbag are SR relativistic Doppler Effect and gravitational redshift. Since neither of these effects can do the job alone, the solution seems to lie in combining them properly.

A.B. Whiting may have been on the right track when he derived the gravitational component of cosmological redshift in a universe with static gravitational density by calculating the difference between the matter density now and zero matter density. As he says, just multiplying the SR Doppler redshift and the gravitational redshift together calculates the correct instantaneous cosmological redshift for a flat FLRW universe with static density.

I think the remaining step needed to extend his analysis into a general equation for cosmological redshift is to perform an integration of the SR Doppler redshift at each point between the emitter and receiver, multiplied by an integration of the gravitational redshift at each point between the emitter and receiver (with matter density varying from that at emission to zero now.) Something like this:

$$\frac{\lambda_{r}}{\lambda_{e}} = \int\begin{array}{cc} v^{r}\\v_{e} \end{array} SR \ Doppler \ redshift \\\ \int\begin{array}{cc} 0 \\\rho_{e} \end{array}\\\ gravitational \ redshift$$

I want to emphasize that, unlike my earlier attempt at a solution, I do not think a separate element should be included to account for clock rate differentials. The change in matter density as a function of time does not cause any clock rate differential in the homogeneous FLRW metric. In normalized units, the FLRW metric can be simply written as:

ds2 = -dt2 + a2(t)(dx2 + dy2 + dz2)

The cosmic clock (t) is invariant for purely comoving observers as a function of the declining matter density. The cosmic clock is just the timelike spacetime distance orthogonal to a hypersurface of constant comoving physical distance, so:

ds2 = -dt2.

So in the same way that the declining cosmic matter density does not create any gravitational redshift, it also does not create any clock differential between the emitter and receiver.

Conclusion

Hopefully these thoughts are broadly consistent with the eventual solution I think must inevitably be derived to provide an comprehensive alternative explanation of superluminal recession and cosmological redshift without resorting to the concept that space itself is expanding.

Jon

Last edited: Jul 23, 2008
2. Jul 23, 2008

marcus

It was a constructive step to rearticulate your position and start a new thread. You are right that there is no one global Lorentz frame. The universe can't be put into a fixed SR context.

However you attribute this to the presence of gravitating matter. You say you are considering the case of Lambda > 0. The de Sitter universe doesn't naturally fit in a global Lorentz framework and yet it has no matter. So that might be something for you to think about.

As matter thins out, our universe is expected to approximate a deSitter universe more and more closely. That doesn't fit an SR frame. It has just as much superluminal expansion as we do now. You haven't shown that the region becomes converted to a true SR-compliant global frame.

You want Hubble Law to cease as matter thins out, I guess, or for the parameter to go to zero. I gather it is expected that in the late time universe the Hubble Law parameter will approach something like 60 km/s per Mpc. Percentage increase of large distances will level out from the present roughly 1/140 percent per million years to about 1/160 of a percent per million years. You'd need to show your claim mathematically. Maybe one of the others can give you some advice as to how to proceed with that.

You haven't yet shown that superluminal recession is an observational artifact. So the rest seems moot:

We have no evidence it is an artifact, but it is good you are asking how the cosmological redshift comes about---what the mechanism is. It is possible to think of a lightwave as making transitions from one local frame to another. Some people think like that. But in my opinion it isn't very physical. Local frames are a human construction. They are something we imagine, not something physical. I prefer to think of the redshift happening in a slightly different way---Maxwell's equation (the usual electromagnetic wave equation) operating is a context where distances increase slightly as the wave undulates thru. But it is just a question of taste really. Wave propagation a la Maxwell is a geometrical phenomenon. I think of the geometry of the E and B fields in a space where distances gradually increase. I just don't like to objectify a big bunch of local frames as if they were a real thing---they are something humans use to approximate and compute with.

Personally I dont say "space expands", the reason is I don't like to objectify space, make it seem to people like a substance or a real thing.
I also refrain from saying "space does not expand". that would be an even more counterproductive thing to say. The Einstein equation is about DISTANCES namely it is a differential equation governing the evolution of the metric. So one can clearly say that distances expand, in our universe. It is basically what General Relativity is about.

I don't see the point of your alternative explanation, Jon. I understand superluminal recession and cosmological redshift easily simply in the context of systematically increasing distances (according to the Einstein equation). I don't resort to saying space itself is expanding---that phrase strikes me as something of a strawman or a red herring, somehow. Something fishy. Given the choice I suspect I'd prefer people would just think of space as expanding rather than imagine that they have to make up alternative explanations such as the present one.

At any rate, an interesting attempt. And I think it was time to revise and restate your ideas in a new thread.

Last edited: Jul 23, 2008
3. Jul 23, 2008

jonmtkisco

Hi Marcus,

I offer faint thanks for your faint praise.

I did not claim to prove that superluminal recession is just an observational artifact, I said the logic of the scenario suggests the possibility.

It doesn't help achieve my scenario if the Hubble velocity peters way out. I need recession velocities to remain superluminal across a spatial interval small enough to have a legitimate possibility of containing vanishingly close to zero particles (and therefore effectively zero gravity) at some far future date.

I'd prefer to use the example of a matter-only Einstein-de Sitter universe with Lambda=0. Then an unadulterated SR global frame could exist within some finite subdomain. However, that equation may not close, because the further the particles are apart, the more they've already been slowed by gravity, and there may be no superluminal particles left at the opposite borders of any region small enough to be reasonably devoid of gravity.

A common scenario describes that in the far future, the great majority of ponderous matter will consolidate into widely scattered supermassive black holes. If that occurred at late times in an Einstein-de Sitter universe (Lambda=0), it would increase the opportunity for a pair of BH's to be receding from each other superluminally for a limited time, with vanishingly little matter density remaining interposed between them. If that scenario worked out, it would strengthen the argument that superluminal recession might not be physically real.

In the de Sitter model, of course the exponentially accelerating recession velocity itself does not disqualify it from being a pure SR global frame. Instead it's just the gravity of Lambda, and maybe also the negative pressure of Lambda. So I'll probably give up on trying to use any scenario with Lambda.

Of course it's quite possible that superluminal recession is a physically real phenomenon, at least judged by some standard of reality. We also should consider the possibility that any rulers we use to measure recession velocity may have experienced Lorentz contraction.

Others are welcome to help think about how best to explain superluminal recession and cosmological redshift without resorting to the notion of expanding space. I hope none of us considers this subject to be unworthy of brainstorming.

Jon

Last edited: Jul 23, 2008
4. Jul 24, 2008

jonmtkisco

Thinking more about whether superluminal recession might or might not be a physically real phenomenon...

Consider the scenario of a very underdense, matter-only universe (Lambda=0) with the negative spatial curvature specified by the FLRW metric. At any given radius from an observer at the center of her observable universe, galaxies recede faster than the escape velocity of the mass/energy contained within that radius. Compared to a flat universe, recession velocities are relatively high compared to the contemporaneous matter density. At some point in the late history of this universe, it seems likely that two galaxies (or particles) will have superluminal relative recession velocity, with vanishingly little matter (and therefore gravity) in the region between them. That region then qualifies as an SR global frame, so here we might expect to achieve a violation of the SR speed limit of c.

It seems to me that one of two possible conclusions applies here.

1. Superluminal recession is actually an observation artifact rather than physically real, or

2. Mother Nature doesn't like negative spatial curvature, and won't let this situation occur.

I said in the first post that GR's applicable metric dictates by how much a local frame may violate the speed limit of c compared to another local frame depending on the cosmic gravitational density and distance between them. I see nothing in GR itself which directly controls this; it is the FLRW metric which controls it, but it is not an absolute control.

If you want to have flat spatial curvature in an FLRW universe, you can exceed the speed limit by only so much, as a function of gravitational density and distance. Exceed it by more than that, and the FLRW metric forces you into negative curvature. But with enough spatial curvature, apparently it is possible to exceed the speed limit by an arbitrary amount within an arbitrarily small distance, with an arbitrarily low gravitational density.

Maybe one could rationalize that clocks run slower in negatively curved regions than in flat regions, so the recession speeds are actually lower than they seem. But, other factors being equal, calculated recession speeds in the FLRW metric increase when the curvature goes negative, they don't decrease or top out. In fact if they decreased so as to offset a possible clock difference, it might never be possible for the metric to calculate the existence of negative curvature. Which is a problem that the metric clearly doesn't suffer from.

I suppose one valid question is, if the very large but finite region between the two galaxies (or particles) is devoid of matter and gravity, how can that region have negative spatial curvature? Something about this situation seems circular. Yet isn't there still a violation of the SR speed limit even if that finite region is inferred to have become spatially flat?

Jon

Last edited: Jul 24, 2008
5. Jul 25, 2008

Chaos' lil bro Order

Great post Jon, it was a pleasure to read.

There are some very interesting ideas I've never heard in there before. In particular, if I am understanding one of your points correctly, you have described a possible 'solution' to the cause of dark energy accelerating properties with respect to the Universe's expansion. Which I'm interpretting as a scenario where a Big Bang event occurs and because the Universe's density is so great at this epoch, say the first 1s, that gravitational effects dampen the Universe's acceration as a form of 'gravity braking', and that as time progressed thereafter, the gravitational effects lessened with the thinning of the Universe's overall density. So in effect, the Universe that we think of as accelerating may be rather like a car driver easing his foot off the brakes whilst holding his other foot at a constant 100km/h. Maybe the Big Bang for lack of a better term, exploded with a force that remained constant.

Could dark energy be explained as the thinning of gravitational braking? We know the gravitational force was the first of the 4 forces in the Universes, so the gravitational braking would be especially high when there was no EM force to provide counter pressure, as in neutron stars and such. The Inflationary period could possibly be explained as the period between the gravitational force and EM force? I think of the EM force as a passenger in the car leaning over the driver's lap and lifting up his foot off the break slightly. Of course these analogies only get you so far and you must back up any claims with mathematic proofs.

I don't know, but it was a interesting post to read. Cheers.

6. Jul 25, 2008

Janus

Staff Emeritus
In your car analogy, the foot on the gas Is dark energy. An analogy that fits a universe without acceleration of the expansion would be closer to this:
Start with a car initially moving 100kph, coasting and with your foot on the brake. Then ease up on the brake as time goes on. The car continues to slow as time goes on, but the rate at which it slows decreases.

This analogy matches what we would expect to see in a universe without dark energy. The decreased effect of gravity is something fully expected. In fact, this is what was bieng investigated in the study that first indicated the acceleration. They were, in essence, trying to determine how fast the universe was "letting up on the brake". What they found was that the universe apparently also had its "foot on the gas".

So while your analogy does fit the presently understood situation, it doesn't "explain" dark energy, because it doesn't explain were the "foot on the gas" comes from.

7. Jul 25, 2008

marcus

I find myself enjoying these posts too, as an example of able courtroom argument. Concerns about the physical content or lack thereof, though. Maybe, Chaos' lil, since you read the first post you can tell me how you take the following.

I'd like to hear an independent check from someone else besides the author. So here it is. This is the main point---the rest depends on this.

As far as I can see, physically speaking the reasoning here is vacuous (although as a courtroom argument or legal brief it is very nicely argued!) If you disagree, Chaos-lil, please explain--I'd like to hear your take.

BTW I have highlighted in red a key statement which seems in error. When density thins out in some finite piece of the universe it does not necessarily give rise to an SR-compliant region of spacetime.

==quote with blue comment==
If the gravitational density is low, the degree of "violation of the speed limit" in nearby frames is infinitesimal. If the gravitational density is high, this speed limit can be "violated" to a larger degree.

associates FTL recession with the circumstance of high density

Consider our very early observable universe, ... The FLRW metric ... calculates that matter particles located just millimeters away from each other were receding from each other at velocities many times faster than c. This demonstrates that a tiny distance between distinct local frames is no inhibitor to observing a massive "violation" of the SR speed limit. All that’s needed is truly astounding gravitational density -- which is what theory calculates for our very early universe. ...

not true high gravitational density is NOT all that is needed, nor is it sufficient. it just happens that in this example there is a circumstantial association between FTL recession and high density

One must confront the question whether superluminal recession is a “physically real” phenomenon or just an observational artifact. ... when gravitational density drops to zero in a given large but finite region, as it eventually must, how can superluminal relative recession velocities remain possible from one end of that region to the other, regardless of how widely separated the two particles are? Within its bounds, that region has in fact become converted to a true SR-compliant global frame. This logic suggests the theoretical possibility that superluminal recession is not physically real and might be an observational artifact.

Look at the boundary conditions of the region. Just because a region is nearly empty does not mean it is flat.
You can't fit an SR-compliant frame to a region just because it has low density----if the boundary has nontrivial geometry this will affect the geometry of the region.

If superluminal recession is merely an observational artifact, then ...

==endquote==

Everything that follows is based on the assumption IF superlight recession is merely an observational artifact. But that seems moot (empty of meaning) because the initial assumption has no basis. Or at least no basis is provided here.

Last edited: Jul 25, 2008
8. Jul 25, 2008

jonmtkisco

Hi Chaos,

I agree completely with Janus' response to your post.

Think of receding galaxies as being Newtonian cannonballs fired from the surface of the moon (no atmospheric friction). If a cannonball is fired exactly at its Newtonian escape velocity, its speed away from the moon will become slower and slower over time, asymptotically approaching zero when the distance reaches infinity. As a function of increasing distance, the declining force of gravity and the declining velocity exactly balance each other.

Jon

9. Jul 25, 2008

jonmtkisco

Hi Marcus,

I appreciate your substantive critiques as well, even if they are negative in tone and devoid of any contribution on your part about how to explain superluminal recession and cosmological redshift without resorting to the notion of expanding space.
This comment is cryptic so I don't understand why you say my point is wrong. In a flat matter-only expanding universe (Lambda=0), the FLRW metric does not permit superluminal recession velocity to exist without either a lot of gravitational density or a combination of lesser density and very large distances. It's dictated by the GR metric, so how can it be merely a circumstantial association? This is exactly the point I'm trying to make.

If you're referring simply to the fact that something causing geometric expansion rates (like inflation) is needed to impart the original superluminal recession velocities to the particles, I agree with that. Other than in a de Sitter-like universe with a dominant cosmological constant, some force is need to impart an initial velocity to the particles, and it needs to impart relative velocities that are superluminal from the start. But those superluminal initial velocities are not merely curious optional features of a (nearly or entirely) flat universe with the gravitational density and Hubble rate we have; the FLRW metric makes them mandatory for us.
That's a valid qualification but I think it's not a fatal one. Yes if there's a significant amount of matter hovering near the boundary of the region, it will gravitate into the region, adulterating the region's SR purity. One can address that by referring to two extremely tiny test particles (instead of galaxies or black holes) which are receding from each other at superluminal velocities, and ensuring that the vanishingly empty region extends well beyond the test particles, not just directly between them.

Jon

Last edited: Jul 25, 2008
10. Jul 25, 2008

jonmtkisco

Here is a rejiggering of the cosmological redshift equation I suggested, which is simpler and I think is more mathematically accurate:

$$\frac{\lambda_{r}}{\lambda_{e}} = \int\begin{array}{cc} t_{r}\\t_{e} \end{array} \left( SR \ Doppler \ redshift \left[v_{rec \left( t \right) } \right] \right)\left( gravitational \ redshift \left[ \rho_{t} , 0 \right]\right) dt$$

where: $$\lambda$$ is wavelength, $$v_{rec \left( t \right) }$$ is recession velocity at each time interval, $$\rho_{t}$$ is density at each interval, and gravitational redshift is calculated as between current density and 0 density at each interval.

Jon

Last edited: Jul 25, 2008
11. Jul 25, 2008

jonmtkisco

It strikes me that at any given Hubble rate, the less gravity density there is, the easier it is to sustain a higher proportion of the receding galaxies at superluminal recession velocities over a long period of time, and vice versa.

Doesn't it seem like it should be the opposite: At any given Hubble Rate, the less gravity density there is, the less likely superluminal recession would be, and in the limit of vanishingly small gravity (an SR global frame) there would be no superluminal recession at all?

Edit: Well maybe the problem is that this concept of duration is too superficial. Other things being equal, a very underdense universe will arrive at our (current) density and Hubble rate after much less elapsed time than an overdense universe would. But even so, once the parameters reach those values, a very high percentage of the galaxies will thereafter remain at superluminal velocities for all eternity. Whereas in a very overweight universe, even after our parameter values are reached, the recession velocities of many more galaxies will thereafter progressively drop to below c. Hmmmm.

Jon

Last edited: Jul 25, 2008
12. Jul 25, 2008

marcus

Jon, let's focus on the core of your argument and make sure I understand just what it is you are saying. As I see it you consider two cases. The first one (post #1) has Lambda > 0 and the second case (post #4) has Lambda = 0 and Omega < 1. I will quote and then try to paraphrase you as clearly as I can..

In both cases you want to argue that FTL recession doesnt really happen---is illusory. The way you argue this is by constructing an apparent contradiction.

Here's the first case (post #1)
First as a technical point, in the Friedmann model the density never drops to exactly zero. Nor is that realistic, there is always some matter in between galaxies. So we had better say the density of matter approaches zero. That is not a criticism of you, just clarification.

Now the argument goes as follows: consider a large but finite region of space S.
and a time-interval I in the late universe
and construct a big finite chunk of spacetime SxI (Friedmann model coordinates help here)

You say: if the interval I is chosen late enough, S will be nearly empty of matter.

Therefore we can approximtely fit the block of spacetime SxI with an SR-compliant frame!

Ahah! you say. Two galaxies with this nearly empty block can't be receding FTL from each other.

Then, in a separate argument, you may hope to show that if FTL is illusory in the late universe it could be dubious in the present as well. I'm not sure how that would go.

But anyway I think we disposed of that argument in post #1. What made it a no-brainer was Lambda > 0. Because there was dark energy, the spacetime block SxI turned out to be approximately congruent to a chunk of deSitter space. deSitter space is a 4D spacetime in which there is no matter at all, and yet FTL expansion goes on forever.

===========================================================

So now we have to consider your second case (post #4). this time you make essentially the same argument but with dark energy out of the picture. You put Lambda = 0, and you say underdense which I guess means total Omega < 1.

Again you use the Friedmann model obviously. Again you go for a large finite chunk of spacetime SxI which is nearly empty. Density cant be assumed exactly zero, but as close to zero as you think you need just by going far enough out.

If I understand you, you are trying to get a contradiction. The Friedmann model tells you that there are two galaxies, say at opposited sides of this big nearly empty region S, which are receding FTL from each other. BUT you say, this big chunk of spacetime SxI can be approximately fitted with an SR-compliant frame. Ahah! Contradiction!

In courtroom terms, this raises doubts in the jury's mind. Maybe the FTL recession isn't real. Could it be just an illusion---an artifact of how we observe?

Then I guess you could be planning to work back---if FTL is unreal in the late universe maybe it is illusory even now, at the present day. You've given some arguments elsewhere as i recall, along those lines.

Now, is this an accurate sketch of how you are arguing the case?

I'm anxious to get it boiled down to brief, and make sure I understand.

13. Jul 25, 2008

marcus

In the second case, the argument also breaks down. It breaks down where you say It seems likely

You take a region S of fixed size. To get a SR frame to approximately fit you need to go far out in the future, so (for example) the density gets very small.

But the Hubble parameter is going down as well, so as the density gets very small you also find that there is no more FTL recession between pairs of objects in the region. So there is no contradiction.

The attempted argument is by contradiction, you are trying to show that while the Friedmann model shows FTL this is inconsistent with fitting an SR frame onto a region in late universe. But the contradiction doesnt emerge because you arent getting FTL from the Friedmann model.

14. Jul 27, 2008

jonmtkisco

Sorry to do this again, but my suggested equation for a bottoms-up calculation of cosmological redshift needs to be tweaked again. Hopefully this is the last tweak.

$$\frac{\lambda_{r}}{\lambda_{e}} = \int\begin{array}{cc} t_{r}\\t_{e} \end{array} \left( SR \ Doppler \ redshift \left[ \frac{ \left( V_{emit} + V_{rec} \right) }{2} \right] \right)\left( gravitational \ redshift \left[ \rho_{t} , 0 \right]\right) dt$$

where: $$\lambda$$ is wavelength, $$V_{emit}$$ is the proper recession velocity between the emitter and receiver at the time of emission, $$V_{rec}$$ is the proper recession velocity between them at the time of reception, $$\rho_{t}$$ is density at each interval, and gravitational redshift is calculated as between current density and 0 density at each interval.

The reason for this change is that the SR Doppler redshift value should remain constant at each interval over which the gravitational redshift integral is constantly changing. The SR Doppler Effect component should measure only the final net velocity difference between the emitter at emission time and the receiver at reception time.

Jon

15. Jul 27, 2008

jonmtkisco

Hi Marcus,

I think your description of what I said is fairly accurate. I explicitly set aside the idea of using Lambda>0 after the first post in this thread, because Lambda gravitates. All of the subsequent posts have Lambda=0.
I made exactly this point in my second post, in which I lamented that I probably couldn't arrange the empty-region scenario I want in a flat FLRW universe. In subsequent posts, I introduced the scenario of a very underdense universe with large negative spatial curvature. In that model, recession velocities can remain arbitrarily high for an arbitrarily long period of time. So it seems probable to me that a valid theoretical scenario can be arranged where two particles with Superluminal mutual recession velocity are embedded in a large but finite region containing no other matter.

I agree that regardless of how underdense it is, by definition an Einstein-de Sitter universe would not be entirely empty of matter. But I never suggested that the entire universe was empty; I was describing only a large but finite region which is either empty (other than the two test particles) or vanishingly close to empty. The existence of such a region in a very underdense universe "in the distant future" does not seem to offend the metric at all.

Please don't get me wrong, I'm not claiming to have "proved" a contradiction. I'm just saying that the logic suggests the possibility of a contradiction. This logic isn't limited to the special case where a region contains zero matter; a countervailing overall pattern emerges from the general metric. If we increase the matter density while keeping the Hubble rate constant, it becomes increasingly difficult to sustain superluminal recession velocities at all for any long period of time. One might have expected the opposite, if gravitational density is indeed the primary enabler of superluminal recession.

This countervailing pattern also raises the possibility that there may be NO satisfactory explanation available for the seemingly unprincipled nature of superluminal recession, other than that it is possible ONLY because of the expansion of space itself. But I think it's fair to say that current mainstream cosmology has not declared this to be the only reasonable answer, so why should we throw in the towel so quickly?

Jon

16. Jul 27, 2008

Sundance

G'day from the land of oz

Interesting reading on intrinsic redshift

http://arxiv.org/abs/astro-ph/0603169
Six Peaks Visible in the Redshift Distribution of 46,400 SDSS Quasars Agree with the Preferred Redshifts Predicted by the Decreasing Intrinsic Redshift Model

Authors: M.B. Bell, D. McDiarmid
(Submitted on 7 Mar 2006)

http://arxiv.org/abs/astro-ph/0409215

The Discovery of a High Redshift X-ray Emitting QSO Very Close to the Nucleus of NGC 7319

Authors: Pasquale Galianni, E.M. Burbidge, H. Arp, V. Junkkarinen, G. Burbidge, Stefano Zibetti
(Submitted on 9 Sep 2004)

17. Jul 28, 2008

jonmtkisco

Hi Sundance,
Thanks for the reference to the papers. It's sobering to be reminded how much effort goes into distinguishing real phenomena from data selection biases.

Jon

18. Jul 28, 2008

Sundance

G'day from the land of ozzzzzzz

jonmtkisco said

How do you distinguish?

19. Jul 28, 2008

Chaos' lil bro Order

Ok Janus, now you are just confusing me. Unlike many cosmologists, I don't find it offensive or incorrect to say that the Big Bang was an 'explosion' that was comparable to how a spherical shaped charge of C4 explodes. However, unlike C4, the fragments of the big bang were of such high density during the first few seconds after the explosion that they gravitationally dampened the massive expansion. As the explosion grew, the proximity of one fragment to another fragment diminished, and thus gravity's inverse square law dictated that the gravity 'felt' between any two fragments also weakened. And weakened and weakened and weakened. The Universe 'appeared to be speeding up' in its expansion, but in reality it just had less gravitational breaks slowing it down. Anyways, that is the theory as I understood it. I am not expert enough to judge it on its consistencies or inconsistencies with cosmological data, so I defer this to smarter people than I, like Janus and Marcus. Help :)

I think its also important to note that we have no idea if the Universe big banged into a medium that would have caused any friction or other effects on the accelerating Universe. Clearly a C4 explosion which takes place in air, explodes with its highest velocity upon ignition and its fragments then decelerate according to earth's gravity and the friction caused by earth's air.

If I'm understanding it right, it is quite a nice theory and worthy of consideration. Some questions come to rise: Do cosmologists know or have limits set on the Universe's accereration rate? If so, is the Universe accelerating faster or slower than the square law (ex. 1,4,9,16,25...). If faster, clearly the weakening of the gravity breaking alone could not achieve this, so one then adds another force to the Universe as an additional boost to the Universe's acceleration. Dark energy, Quintessence, etc. Or, one could imagine a Universe that exploded with an intrinsic force that is accelerative in its very nature and that the gravity breaks have never stopped the Universe's accelerated expansion, but they merely have dampened it less and less over time.

Janus, Marcus what contradicts this theory?

Last edited: Jul 28, 2008
20. Jul 29, 2008

jonmtkisco

Hi Sundance,
Well, the two articles you referenced show examples of how cosmologists try to approach the issue. For example, if you have two independent data sets obtained through different techniques, the likelihood of both having the same data selection bias may be reduced. Known selection biases can also be subtracted out. And sometimes people just make judgements from the shapes of the curves, as to whether a selection bias seems plausible or not.

At the end of the day, increasing the amount and diversity of data sources is the way to figure it out. That may take years or sometimes decades.

Jon