# Void theory vs. acceleration

1. Nov 5, 2008

2. Nov 5, 2008

### MeJennifer

First cosmologists claimed that the FRW model was a good approximation for the universe we live in, then we needed dark energy, when that was not enough we needed dark matter, now it seems we need more outlandish options.

3. Nov 5, 2008

### Garth

Not necessarily outlandish.

The FRW model assumes homogeneity on the largest scales, however on smaller scales there are lumps, such as ourselves, stars, galaxies and galactic clusters.

Where matter has clumped into large scale structure it is to be expected that relative voids have been left behind.

The question is just how large do these large halos and the subsequent voids get?

The interpretation of the data is model dependent.

Where a model assumes homogeneity over the largest presently observable scales and therefore at these scales the Copernican Principle applies to the Earth, then the present data requires Dark Energy, or just possibly a modification to GR theory, to explain the fainter-than-expected SN 1a.

If however you change the assumption and hypothesize that the Earth happens to be a large void then the present data could be explained without DE or a modified theory.

If we are able in future to measure standard candles out to larger distances and reach the hypothetical limit of any supposed void, then the issue should be resolved.

Garth

4. Nov 5, 2008

### Hurkyl

Staff Emeritus
You say that like it's a bad thing.

5. Nov 5, 2008

### marcus

Good points Garth!
No, certainly not outlandish
If I'm not mistaken, this alternative explanation has been obvious from the start and has been championed over the years by a small number of people, notably
David Wiltshire. The contribution made by these people (Clifton et al) seems mainly to consider how to test the idea.

http://arxiv.org/abs/0807.1443
Living in a Void: Testing the Copernican Principle with Distant Supernovae
Timothy Clifton, Pedro G. Ferreira, Kate Land
Phys. Rev. Lett. 101 (2008) 131302
4 pages, 3 figures.
(Submitted on 9 Jul 2008)

"A fundamental presupposition of modern cosmology is the Copernican Principle; that we are not in a central, or otherwise special region of the Universe. Studies of Type Ia supernovae, together with the Copernican Principle, have led to the inference that the Universe is accelerating in its expansion. The usual explanation for this is that there must exist a 'Dark Energy', to drive the acceleration. Alternatively, it could be the case that the Copernican Principle is invalid, and that the data has been interpreted within an inappropriate theoretical frame-work. If we were to live in a special place in the Universe, near the centre of a void where the local matter density is low, then the supernovae observations could be accounted for without the addition of dark energy. We show that the local redshift dependence of the luminosity distance can be used as a clear discriminant between these two paradigms. Future surveys of Type Ia supernovae that focus on a redshift range of ~0.1-0.4 will be ideally suited to test this hypothesis, and hence to observationally determine the validity of the Copernican Principle on new scales, as well as probing the degree to which dark energy must be considered a necessary ingredient in the Universe."

As far as I can see the essence of the FLWR model is that it is a workable application of GR---you make simplifying assumptions of uniformity (iso. and homog.) and start trying to fit.
Maybe at some point you find you need to slightly weaken the uniformity assumptions. Maybe the surrounding matter is not perfectly uniformly distributed, maybe we are in a region that is a few percent sparse. OK that is a judgment call. A consensus would have to build up that this is the most economical way to improve the fit to the data.

The point is the model would still be essentially the FLWR, still be essentially General Relativity with simplifying assumptions of (near) uniformity. Nothing exotic here. We would just be acknowledging that deviations from the uniform distribution of matter, which earlier were thought to be too small to be important, actually were large enough to be important.

IIRC David Wiltshire was already offering this explanation some 4 years ago, like 2004 or 2005. The difference is, AFAIK he didn't stress the aspect of testability, at least not enough to make an impression. It was somehow too nebulous. Nobody likes ideas that can't be tested. And these people are selling us on the idea that all we need to do is make some more supernova measurements, on some comparatively nearby supernovae, and we will actually be able to rule out this void (really just slight sparseness) idea, if it is wrong. Anyway that's my take.

Last edited: Nov 5, 2008
6. Nov 5, 2008

### marcus

Indeed cosmologists as a group are exceptionally open to novel ideas, so in the context of conventional cosmology we'd have to say outlandishness is a good thing. :rofl: One could even accuse them of being too fond of proposing and arguing for unorthodox ideas.

I think Jenny misidentified this (local sparsity) idea as outlandish---it strikes me as pretty tame. The main features of a GenR picture of the cosmos would remain. People who are constitutionally incapable of accepting c+ increase in distance between objects at CMB rest would still find the same difficulty accepting the universe.

One would just have found a different way to tweak FLWR and I fear the same people would continue to deem it indigestable for the same reasons

7. Nov 5, 2008

### Chronos

Whatever works is fine with me. So far I've seen nothing that works better than the mainstream model that does not suffer a fatal deficiency [e.g., observational evidence that refutes the alternative model more thoroughly than the mainstream model]. The beauty of the mainstream model is its robustness in the face of unexpected, new observations. While not complete, it is not fundamentally flawed [IMO].

8. Nov 6, 2008

### MeJennifer

A FRW solution is merely a particular solution of a possible GR universe. The assertion that a FRW solution is not a good approximation for our existing universe does obviously not invalidate the claim that our existing universe is a, what you call, "GenR picture".

9. Nov 6, 2008

### mysearch

I am not in position to deny or support this claim, but do have some questions about the basic LCDM model of a fairly fundamental nature. As I understand it, the basic model appears to be supported by the Friedmann equation set. This in-turn seems to be predicated on the energy density of just 4 main components as a function of time, i.e. baryon matter, radiation, cold dark matter and dark energy. Given some of the comments regarding dark energy in this thread, I guess some aspects of this model should still be regarded as ‘speculative hypothesis. For reference, I have laid out how the energy density seems to change with time in the following thread:

I realise my model is simplistic, but does it represent the basic principles thought to be at work?

While dark energy, based on the assumption [w=-1], does lead to an expansion from 6-7 billion years onwards, it doesn’t seem an adequate explanation of the expansion before this time. In fact, the model, based on Friedmann equations, appears to only describe a universe that can collapse under gravity. Possibly, this is why the ‘recessional’ velocity associated with the Hubble constant [H] appears to align the free-velocity of an object falling from infinity under gravity. As such, the Friedmann equation doesn’t seem to describe the expansion of the universe, only its contraction played backwards in time!

Another area of confusion relates to the standard big bang model, which always stresses the importance that it is not an explosion, but rather the unit expansion of space. As such, this type of explanation doesn’t seem to leave much room for a classical concept like momentum to maintain the expansion of the universe after some initial expansion effect, e.g. inflation.

So how does cosmology explain the expansion from 1 second to 6 billion years?
Is there a dark something else lurking around?

I am hoping from the sum total of all your contributions that you are the right people to ask.

10. Nov 6, 2008

### marcus

May I jump in here with a reply? Your question is to Chronos and I'm hoping to see his response as well but I want to comment.

There is good and bad news. The good news is there is a simple answer----what keeps the expansion of metric distances going, once started, is Einstein equation.

The bad news is two things:
1. We don't have a deeper explanation of why Einstein equation. Not yet.
2. We don't have a sure explanation of how distance expansion got started. Not yet.

(Those are two reasons so many people are working on quantum gravity and quantum cosmology now. Better measurements will probably allow testing some ideas in the next few years, which is another reason research effort is building.)

--------------------------
In our current understanding, geometry is not the same as matter. Momentum is an idea in the mechanics of matter. Why should geometry have any analogous quantity?

You seem to be asking for a mechanics explanation for the fact that geometric change continues. What makes it keep on expanding?

You think you understand momentum. Do you? What gives matter its inertia? Why does matter in motion continue moving? We do not understand. We have only gotten accustomed to the idea since Galileo and Newton told us about it. Newton wrote an equation: force is change in momentum, no force=no change in motion. That equation is about as deep as our notion of momentum goes.

The Einstein equation is a parallel business. Geometry (represented by the metric) continues evolving on its own but this evolution can be influenced by some matter, on the righthand side, if there is some. The fact that an empty universe's geometry will continue evolving in the absence of matter is no more or less mysterious than the fact that one of those spherical Russian tea cakes covered in powder sugar will continue moving in the absence of force.

One idea is more familiar but both are essentially mysterious. At present.

11. Nov 6, 2008

### mysearch

It is not clear to me how Einstein’s equations explain anything until you infer some physical description to its abstraction. Normally, Einstein’s tensor represents the spacetime geometry linked to the stress-energy tensor. In the context of Friedmann’s solution, the stress-energy tensor appears to be equated to an energy density within a given volume of space. As such, Einstein's equations would equate the curvature of spacetime to the energy and momentum within the spacetime. However, the current array of prospective energy densities, i.e. baryons, radiation, cold dark matter and dark energy, do not seem capable of explaining the initial expansion of the universe.

Therefore, it seems that quantum gravity and quantum cosmology will either have to come up with a radical new theory to explain expansion or inject another dark something into the mix. If this is the actual state of play, then I believe the original statement should come with some qualification:

12. Nov 6, 2008

### marcus

If it's not clear yet, then you should keep trying to understand and we should keep trying to help. It may help to point out that a 4D metric that is a solution to Einstein equation (covering a whole spacetime region)

is morally the same as a history of a 3D metric that evolves (given a choice of time parameter etc)

Where the differential equation prevents abrupt creases and cracks of the eternal 4D solution.
and that translates into gradual evolution if you look at the 3D metric evolving thru time.

I've said that the Einstein equation makes 3D geometry evolve smoothly, without abrupt jerks, so that in the absence of matter if it starts out expanding it will continue for a while. Geometric change has a certain degree of persistence. (Although matter can exert a gradual effect----the persistance is to a degree maleable.)

You say you do not understand this, I guess because you are thinking that the equation gives an eternal once-for-all 4D solution, a history of the geometry of the universe. So where does that say persistence?

I answer that the Einstein equation forces the eternal 4D solution to be gradual, a bit like gently sloping ground rather than rough rocky cliffy discontinuous terrain.
And that smooth continuity of the eternal 4D metric guarantees steady persistence when it is translated into a time-evolution of a 3D metric.

Let me know if this helps you understand it better. The thing to realize is that in the absence of matter or anything else, if 3D geometry is started off expanding then it is going to persist. And that will also be true if you add modest amounts of matter. IOW the persistence of expansion does not depend on dark energy or any kind of matter. There is no secret factor. It is how geometry behaves of its own accord.

The mystery is the Einstein equation itself. We would like to have a more fundamental description of the underlying reality, a description from which space, time, matter, geometry and their interrelationships emerge---a more fundamental description from which the Einstein equation can be deduced (instead of merely being tested and accepted as accurate.)

13. Nov 7, 2008

### mysearch

My apologises to Chronos for repeatedly using his comments out of context, but I am only using it to help highlight some of my own confusion:

So what exactly is the accepted mainstream model, i.e. LCDM, and what assumptions underpin this model? My initial starting point was Friedmann’s equations as they were generally referenced as the most important equations in cosmology and a general solution to Einstein’s field equations, hence my comment:

However, I raised my initial questions because my simple model based on Friedmann’s equations didn’t appear to adequately explain the early expansion of the universe. Therefore, has the mainstream model now evolved towards an accepted 4D metric solution to Einstein’s equation? I openly admit that I do not understand the premise (or physics) on which the following statements are based, as I have not had any exposure to these ideas in my general reading of the cosmology model so far:

Therefore, I would much appreciate any links or references that outline the general ideas behind this line of thinking. It would also be useful if some other members could outline their understanding of what is meant by the mainstream model. Maybe this is another issue for are we all on the same page thread. Thanks.

Last edited: Nov 7, 2008
14. Nov 8, 2008

### mysearch

By way of a footnote to the exchanges 9 thru 13. In #9, I made reference to some analysis of the energy density versus time essentially based on the Friedmann model. This model starts from today’s accepted assumptions about the relative densities of matter (4%), cdm (23%), radiation (<<1%) and dark energy (73%). However, my model predicted a roll-off of the relative density of dark energy, such that it would not play any significant role during the first 3 billion years. As far as I can tell, my model aligns to the results provided by the following cosmology calculators, which are often quoted in this forum.

http://www.geocities.com/alschairn/cc_e.htm
http://www.astro.ucla.edu/~wright/DlttCalc.html
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

The first one is particularly useful in correlating the age, redshift and relative densities. For example, at a redshift z=2, age=3.3 billion years, the dark energy falls below 10%, while at z=5, age=1.2 billion years, the dark energy density falls to <1%. As such, these results also suggest that the expansive property associated with dark energy is not capable of explaining the expansion of the universe in its earliest epoch.

However, I am assuming that cosmologists would still support these results based on the observation of redshift and the scale factor a(t)?

For example, the CMB redshift is ~1090 and can be translated to a corresponding scale factor by the equation [a = 1/(1+z)]. This in-turn can be plugged into an equation of the following form, which is the basis of the calculators mentioned above:

$$\Delta t = \frac {\Delta a}{aH_0 \sqrt{ (\Omega_M /a^3) + (\Omega_R /a^4) +(\Omega_\Lambda) } }$$

Of course, this equation is taking no account of what caused the initial expansion or how long it lasted or how it persisted for some 5-6 billion years. While Marcus, in #12, has made reference to the idea of a 4D metric that might explain how “geometric change has a certain degree of persistence”, I have no idea how this form of expansion is being calculated as a function of time. I am also unclear as where to start researching this idea, as there seems to be so many speculative theories in the field of quantum gravity, quantum cosmology, string theory, branes before even getting to the apparently endless supply of different cosmology models.

Therefore, would really appreciate a pointer in the right direction in the sense that the idea, assumption, hypothesis or theory is supported by the mainstream model, whatever that might be!

Last edited: Nov 8, 2008
15. Nov 8, 2008

### marcus

I thought of another way to explain to you why expansion persists of its own accord. Look at the SECOND Friedmann eqn. It is less quoted but there are actually two Friedman eqns and they are both equally important. The one I mean is the one with a''(t) in it. The second time derivative.

a'(t) is the rate of change of a(t). If it is positive then a(t) is increasing. Once increase gets started, and a(t) is rising, it will continue unless something brings a'(t) down. So what we are interested is a''(t) the rate of change in the rate of change.

As long as a''(t) is small, even if it is negative, then a'(t) the rate of increase of distances will not slow down very fast.

The second Friedmann, or sometimes called the Friedmann acceleration eqn. is what tells you what determines a''(t) and it will explain why it is small. That is another way to understand the persistence of expansion.

Expansion does not need anything to make it persist, it does not need dark energy or anything. It persists by itself for a very long time just because of the Einstein equation which governs how geometry changes.

Friedmann eqns are just simplifications derived from the Einstein eqn. So what we are basically looking at is persistence of expansion that is built into the Einstein eqn.

This persistence does not depend on matter. It is in the geometry itself and would be manifest in a completely empty universe. So you should not look for a material cause.
If you want more cause, you should ask "what underlies the Einstein equation?" why is it an accurate description of nature? The answer, of course, is that we don't know yet. We simply know so far that it is very accurate.

In time, some deeper equation will be found, from which the Einstein eqn arises as a useful approximation, and then we will have more ability to explain. For now, I don't see anything you can do besides just accept the Einstein eqn. of General Relativity as an accurate description of how geometry and gravity behave.

Here is wikipedia about the Fr. equations. Notice that they give two, not just one.
http://en.wikipedia.org/wiki/Friedmann_equations

I wrote a'' with a double prime, or double apostrophe instead of with two dots over it because it's easier. The official notation is "a-double-dot"

Last edited: Nov 8, 2008
16. Nov 8, 2008

### smallphi

The problem with the big void of smaller density leading to apparent dark energy term is that we have to be very close to the center of the void, otherwise everything will look anisotropic. Being close to the center is HIGHLY improbable, much more improbable than being in a void at all.

More popular is the other theory that the dark energy is apparent due to the cumulative effects of the light passing through many voids. That avoids the need for us to be in a center of a spherical void. Supporters of that hypothesis have a hard time proving it since the process of matter density averaging is not defined in GR at all. It's not clear how the true metric irregular on small scales but without dark energy leads to the averaged smoothed out FRW metric with dark energy. Depending on how you define the averaging process, you will get different expressions for the apparent dark energy term. The problem is the averaging process in GR can't be defined in a coordinate independent way.

17. Nov 9, 2008

### mysearch

In post #1, TalonD cited an article that discussed the idea that a void bubble might offer an alternative solution to dark energy being the underlying cause of accelerated expansion. Subsequent posts then debated the pros & cons of the mainstream model and variations on this theme without necessarily being too specific about the definition of what is the mainstream model. While I realise that leading edge research may be too complex to even be summarised in the format of this forum, I would still be interested to known if there is any accepted approximation of the model. Given the general acceptance of the results from a number of cosmology calculators, I assumed that a model based on the Friedmann equation set must still be a valid approximation. However, my analysis of this model raised some questions that I am finding difficult to resolve with dark matter, dark energy, void bubbles or anything that I have read about so far. Given that this seems of fundamental importance, I would like to follow up on the comments in #12 and #15 in a subsequent post. However, apologises if this is somewhat tangential to the main theme of this thread.

Last edited: Nov 9, 2008
18. Nov 9, 2008

### mysearch

While I accept that much may be hidden in the complexity of Einstein’s field equations, usually simplifications are a reasonable approximation of the actual results and reflect the physics by which they are calculated. Marcus, in #15, cited the acceleration equation, which along with the fluid equation, make up a set of 3 equations that allow the Hubble constant [H], rate of change of energy density and acceleration to be calculated. The following equations are rationalised to energy density using the equation of state for each density components, i.e. $$P=\omega \rho c^2$$:

Friedmann...: $$H^2=(8/3) \pi G ( \rho_m + \rho_m + \rho_{\Lambda} )$$

Fluid….….....: $$\dot\rho = -3H \rho (1+ \omega)$$

Acceleration: $$\ddot a/a = -(4/3) \pi G \rho (1+ 3 \omega)$$

Typically, many models assume [matter w=0], [radiatio w=+1/3] and [lamba w= -1] and the results for each of these equations are shown in the attachments below. These results appear to align to the accepted cosmology calculators and the crossover from positive to negative expansion rate occurs at ~7 billion years, which I have seen referenced in standard material. What I don’t see in this simplification is any explanation of why the universe expanded or the persistence of the expansion for 7 billion years in the face of overwhelming gravitational effects.

While I accept that the answer may be buried in the complexity of general relativity and 4D geometry, is there no translation into a more mainstream model?

Therefore, I have to admit as to remaining puzzled by the sentence:

While I guess I may have to give up on this line of questioning, I would still appreciate any clarifications or links that would help me address the following:

Is the implication that matter, cdm, radiation and dark energy are material causes and therefore cannot/do not explain expansion?

If so, is there any cause that can be rationalised and understood by those not so familiar with the complexity and implications of Einstein’s equations?

Thanks

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19. Nov 9, 2008

### marcus

Hi, mysearch. I didn't say the answer was "hidden in the complexity" or "buried in the complexity". So there is no need to accept unreasoningly, or to impute obscurity. It is right out there in the open, at an intuitive level, I would say. If you read simple differential equations, it is in the Friedmann one for acceleration which you just wrote out---I copied it.

For convenience I refer to doubleprime a'' instead of doubledot for the second deriv wrt time.
You can think of a'' as the change in the rate of change.
If there is no matter then rho is zero! So a' doesn't change!
So if a' started out positive, some positive rate of expansion, it just keeps on unchanged!
So expansion doesn't need anything in order to persist! Friedmann tells us this up front.
There is nothing obscure or hidden or buried about it. Friedmann lets it all hang out

You ask for a translation into a more mainstream model. I can't think of how it could be translated into anything more mainstream than first year calculus. a'' is the rate of change of a'.
If a'' is zero then a' does not change, and once started exansion persists. I'm curious, did you get intro to calculus in highschool, or in freshman year college? It would help me to know your background, I don't want to be talking down or over your head either.

It strikes me that your intellectual situation might be similar to that of a fellow in North Carolina who used to post here, I can only speculate. I am anxious to be helpful, just as I was with him---hope you won't take this as condescension and react with resentment. I think it would be a good move on your part, if you don't mind my suggesting it, to simply accept a tendency for expansion of distances to persist and shift over to asking what got it started.

The point is since cosmo is a mathematical science there is nothing more fundamental than the equation model (that checks out against data). If the equation says persistence, that's it, persistence has been explained. There is no more fundamental reasoning.

But the equation in this case does not say how expansion got started. Therefore you can ask to your heart's content about that and never get a conclusive answer--at least for now, people can only offer various untested or unproven ideas like the bounce we have been hearing a lot about lately. And some of these models may be testable when the Planck spacecraft goes up next year (if it is launched as planned) or in any case not so awfully remotely.

BTW typo in your first equation, k-term, doesn't matter to what we are talking about but you might want to fix it.

Last edited: Nov 9, 2008
20. Nov 9, 2008

### mysearch

Hi Marcus,
I don’t think it’s really my maths, although it was a very long time ago, I think it more me trying to get on the same wavelength as you. Some of this stuff is obviously intuitive to you and based on formal training, whereas most of this is new to me. It late here in my time zone, but wanted to ask for a quickly clarification:

I think I understand what you are driving at, but if rho is zero, doesn’t the Friedmann equation suggest H=0 and the fluid equation suggest dp/dt = 0? So when you say no matter, do you also mean no radiation, no cdm, no dark energy?

I can see that you added some additional comments since I started to quickly respond. OK, I guess I will have to accept idea of persistence and the fact that expansion just got started' but it seems to be a model that has no physical basis or explanation of expansion other than it started, it continued and ties up with the Friedmann model at some later time. However, as always, I appreciate your help. I will now go away and read up on some other sources. Thanks