Is the cosmological prinicple wrong? Is Big Bang wrong?

[quantum123]

This is a big hole in the sky. Although you can't see it with the naked eye it actually covers almost 3 degrees of the sky, and to put that into perspective the full Moon covers about half a degree!
Until recently no-one was sure how big or far away this void was but the latest calculations suggest it is 900 million light-years across and 8,000 million light-years away.

So is the cosmological prinicple, which says that the universe is homogeneous and isotropic wrong? Is Big Big theory, which assumes it, wrong as well.?

 

[Chris Hillman]

Don't jump to conclusions!

You are rushing to draw the most drastic possible consequences, but the math by and large supports the general validity of the FRW models as overidealized but good models of the gross behavior of our universe.

As all textbooks stress, the assumption of homogeneity and isotropy used in deriving the FRW models is only an approximation. But you should know that there exist a wide range of exact solutions in gtr which constitute (nonlinear) perturbations of FRW models allowing for a variety of anisotropies or inhomogeneities or both in the distribution of the mass-energy which acts as the source of the gravitational field, and in addition numerical relativists have performed many simulations. Once you know this, you can see that the question should be: how much do inhomogeneities in matter density, possible large and large-scale perturbations, disturb the basic features of the FRW models? Generally speaking, the answer is: not very much. This is why the FRW models --- which are obviously oversimplifications--- nonetheless provide an impressively accurate picture of the gross behavior of our universe on large scales.

 

[Nereid]

This is a big hole in the sky. Although you can't see it with the naked eye it actually covers almost 3 degrees of the sky, and to put that into perspective the full Moon covers about half a degree!
Until recently no-one was sure how big or far away this void was but the latest calculations suggest it is 900 million light-years across and 8,000 million light-years away.

So is the cosmological prinicple, which says that the universe is homogeneous and isotropic wrong? Is Big Big theory, which assumes it, wrong as well.?

(my bold)

One way to test this is to do a great many observations, plot the density fluctuations against scale, and compare what the plot looked like before this 'hole' (it's called a 'void' by astronomers) was discovered with what it looks like now.

http://www.sdss.org/news/releases/20031028.powerspectrum.html" is an example of what the former looks like. I don't have an example of what the latter would look like, but am pretty sure it would be much the same, except that a subset of the three right-most data points would have different (vertical) error bars (probably bigger).

Of course, the plot would be different today in other ways, if only because the WMAP Year 3 results were published after this 2003 plot was published ...

If you're interested, I (or someone else) could dig up some references to the appropriate papers on the power spectrum - just ask; if you're curious, we could walk you through the steps involved in making a plot such as this, at least at a high level (I assume you can see how this plot relates to the 'homogeneous' part of the cosmological principle).

 

[quantum123]

How big must the hole be?

how much do inhomogeneities in matter density, possible large and large-scale perturbations, disturb the basic features of the FRW models? Generally speaking, the answer is: not very much.

How big must the hole be before we can throw away the assumption that the universe is homogeneous and isotropic?

 

[Chris Hillman]

Hi, quantum123,

Looks like you had some trouble quoting something I wrote in my Post #2 above; see https://www.physicsforums.com/misc.php?do=bbcode for was to obtain quotations "by hand" using VB markup.

How big must the hole be before we can throw away the assumption that the universe is homogeneous and isotropic?

Generally speaking, approximations are valid under certain circumstances for certain purposes. An approximation valid for one purpose might not be valid for another. But you shouldn't expect a simple criterion for when a given model is broken "once and for all".

In this case, if you just want to model the gross large scale behavior of our universe, we know from observations that the oversimplified but handy FRW models do quite well. If you are trying to model something like the measured inhomogeneities in the CMB, you obviously can't do that with an FRW model, but a small amplitude linearized metric perturbation of an FRW model might be suitable.

HTH

 

[quantum123]

Ok, let's put it this way.
If you look at the sky 360 degrees all around you and you start to notice one gigantic humongous hole at only one direction, can you still say that the universe is isotropic?
I mean that the universe is homogeneous and isotropic is mentioned in every textbook of cosmology and relativity. This is the material that is being taught to every undergraduate. Is it ok with you?

 

[hurk4]

So is the cosmological prinicple, which says that the universe is homogeneous and isotropic wrong? Is Big Big theory, which assumes it, wrong as well.?

Dear quantum,
Very glad that you bring this question and that we now have all these reactions.

Here is one of mine.
"Cosmological Principle".
As we know, Einstein’s bold idea that the universe is homogeneous in the large scale average is what Milne called Einstein’s cosmological principle. (See P.J.E. Peebles “Principles of Physical Cosmology” page 10). Of course we know that at local scale this principle is not valid.
May I ask the question “what does large scale average really mean?” Is it not so that this has to be seen relatively? So, large scale related to us, can be taken as e.g. the observable universe, but if we relate it to the observable universe, as a kind of entity, then its large scale surrounding/environment will be very, very large.
As far as I have read, there are in fact at least 2 cosmological principles: 1) The perfect cosmological principle of Hoyle and Bondy, which says that the universe is homogenous and isotropic at large scale and at each time. The expansion of the observable universe learned us that this was not the case at each time, so the perfect CP was proven wrong.
2) So there was left Einstein’s CP which seems to be a good starting point for the mathematics of FRLW as an (approximate) language to describe our universe.
In the standard cosmological model, I suppose that, the cosmological principle is indeed taken as base for the classical theory of the universe at absolute large scale and not at a relative scale.
I wonder what the model consequences are if one introduces relativity into the cosmological principle, or is this already done so? If homogeneity, at large scales, in absolute sense, is not a basic ingredient what are then the consequences e.g. for assuming eventual other local concentrations of mass and or energies in our universe other than our observable universe and its environment?
How nice it may be to start with ideal mathematics, I am asking what that does help if in reality one has to do with deviations of those ideal conditions as there are mass and or energy concentrations in the observable universe (and far beyond as I might suppose).
So as a consequence what can bring us Bojowald, Ashtekar, Rovelli if their models are inherent too ideal? Or are they not?
Kind regards,
hurk4

 

[sysreset]

Hurk I believe that although you pose additional questions, you have skirted quantum123's question, which I would rephrase as "what percentage of the observable universe can be an absolute void without violating Einstein's Cosmological Principle?" As a starting point, let's generously put the current discovered void as a 0.5 billion light year radius sphere within the observable universe with a radius of 13 billion light years. Thus, the void only occupies a ratio of 1 to 26 cubed of the universe, which is only 0.00569% of the universe. I do not think that that is a sufficiently high percentage to discard Einstein's CP, although I still wonder what percent would.

 

[Chris Hillman]

Recommend a good course on mathematical modeling

This is the material that is being taught to every undergraduate.

Dunno if you are in school yourself, but if you have the chance to take a course on mathematical modeling, I think this would be extremely helpful to you in better understanding how cosmologists/physicists think.

If you look at the sky 360 degrees all around you and you start to notice one gigantic humongous hole at only one direction, can you still say that the universe is isotropic?

Why take a hypothetical? Sometime after the CMB was observed, it was noticed that it exhibits a "dipole anistropy". But this turns out to be consistent with the hypothesis that we are "moving with respect to the CMB" in a certain direction and with a certain velocity, and after subtracting for this effect, the CMB is once again seen to be, to a very good approximation, isotropic and homogeneous. But after much effort, astronomers succeeded in mappling tiny inhomogeneities in the CMB, so it is known that on a large scale our universe is not perfectly homogeneous.

I mean that the universe is homogeneous and isotropic is mentioned in every textbook of cosmology and relativity.

I can't seem to get this across: theoretical physics is all about idealizations, simplifying assumptions, artful approximations to a more complicated reality by extrapolating small variations from an oversimplified model, and so on. IOW, the aim of all theory in science is to build models with which one can make testable predictions and which one can compare with observation and experiment.

It is well established that the FRW models, while clearly idealizations, do provide a surprisingly good model of the gross behavior of our universe on very large scales. Thus, these models are simplifications, but if all you want to model is gross behavior on the largest scales, they are not oversimplifications.

 

[quantum123]

Can you define what do you mean by large scale? There has to be some clear thinking into this. What size? How many light years is considered large scale? We are scientists here and we want things to be quantified.
Again what do you mean by tiny inhomogeneities? What is tiny? How many lightyears is considered tiny?
Without some kind of quantities, and some math, we cannot start talking about mathematical modelling.

 

[Chris Hillman]

Mentor! Mentor!

Can you define what do you mean by large scale? There has to be some clear thinking into this.

Suppose someone asked: "In the definition of the derivative from difference quotients,
$$\frac{f(x+\varepsilon)-f(x)}{\varepsilon}$$
how small should we take $\varepsilon$?" The answer is: it depends. That is, you need to say something about the nature of f and how much error is acceptable to you; then one can say how small we should take $\varepsilon$! But without that information, one can't say "the answer is that we need to assume that $\varepsilon<1/10$".

If that doesn't work for you, perhaps some mentor can step in because I feel this thread is in danger of devolving into pointless repetition.

 

[Nereid]

Ok, let's put it this way.
If you look at the sky 360 degrees all around you and you start to notice one gigantic humongous hole at only one direction, can you still say that the universe is isotropic?
I mean that the universe is homogeneous and isotropic is mentioned in every textbook of cosmology and relativity. This is the material that is being taught to every undergraduate. Is it ok with you?

Can you define what do you mean by large scale? There has to be some clear thinking into this. What size? How many light years is considered large scale? We are scientists here and we want things to be quantified.
Again what do you mean by tiny inhomogeneities? What is tiny? How many lightyears is considered tiny?
Without some kind of quantities, and some math, we cannot start talking about mathematical modelling.

Earlier I answered your questions by referring to observations, which - I'm sure you'll agree - are the ultimate arbiter in science.

For these new questions, different kinds of answers - in addition to those already given by Chris Hillman - may be of interest.

Take simulations. Have you heard of http://www.mpa-garching.mpg.de/galform/millennium/" ? This - and other simulations - provides one kind of answer: analyses of the (simulated) voids gives you a handle on just how well (or badly) an arbitrary 'gigantic humongous hole' fits within the theory underlying the simulation. And, as Chris Hillman has already indicated, any decision on 'goodness of fit' requires prior decisions on how to measure such goodness, what threshholds to set, and so on.

Another approach: suppose our vantage point were not the surface of our dear Earth; suppose we - intelligent, scientific enquirers - evolved on the surface of Venus, or in the Ganymede ocean; or on a planet orbiting a star in the Arches cluster, or one wandering between galaxies in the Virgo cluster; or somewhere in an ordinary galaxy at the heart of the Shapley supercluser, or a rogue planet at the edge of (or near the centre of) the Bootes void; or ... Could such scientific enquirers have developed a cosmology which included a principle of homogeneity and isotropy? If they were to try to construct a plot like the SDSS one I linked to in my previous post, how different would it be?

You could take an even more extreme 'what if': suppose you were a cosmologist at the time of the radiation-matter decoupling, or 100 billion (co-moving) years into the future, or ... how would your questions be answered then? Or would you, the über-Nobel Prize winning cosmologist, have ruled that homogeneity and isotropy as cosmological principles were completely unsupported by the best observational evidence?

Finally, what do you think about this: the observational basis of contemporary concordance cosmological models is considerably broader than just estimates of P(k)? Or, putting this another way, what role do you think a single observation (or millions of observations of a single object) plays - or should play - in cosmology (as a science)?

 

[quantum123]

If you were to walk along a road one day and fall into a hole, would you complain to the authorities, or say that : hmmm, the road is still homogeneous and isotropic?

 

[russ_watters]

If you were to walk along a road one day and fall into a hole, would you complain to the authorities, or say that : hmmm, the road is still homogeneous and isotropic?

That analogy doesn't work, since we observe roads from close up while the universe's homogeneity is large-scale.

Look, the Big Bang theory is not going to be discarded because one out of a million observations doesn't quite fit one specific, minute piece of it. That just isn't how science works. The fact that there is a large void (assuming it is larger than expected, which I don't actually know) doesn't change the validity of the basic pillars of the theory ( http://www.damtp.cam.ac.uk/user/gr/public/bb_pillars.html ).

 

[Nereid]

If you were to walk along a road one day and fall into a hole, would you complain to the authorities, or say that : hmmm, the road is still homogeneous and isotropic?

russ_watters has already noted that this kind of approach has, it seems, little relevance to how the science of cosmology is actually undertaken, and as we use 'within the framework of modern cosmology, as a science' as our scope here, your post seems way off-topic.

But perhaps that's simply because you wrote too tersely? Perhaps you might like to try to re-cast your question into a form more atune with this section's scope?

 

[SpaceTiger]

If you were to walk along a road one day and fall into a hole, would you complain to the authorities, or say that : hmmm, the road is still homogeneous and isotropic?

Depends on how big the dip is relative to your model of the road. The cosmological principle is never exactly true on any scale and so the FRW model will not be a perfect description of the universe. The observation of an unusually large void might suggest that the FRW model is not quite as good an approximation as we might have thought on scales comparable to the void's size, but it certainly doesn't invalidate the Big Bang.

The real issue is whether or not inflation could explain such a large void, since it claims to predict the initial spectrum of fluctuations. The vast majority of observations done so far support gaussian random phase initial conditions, as predicted by inflation. If it could be shown that the distribution of matter is inconsistent with these initial conditions, then it might bring inflation into question, but it's hard for me to see how it could challenge the Big Bang framework.

 

[sysreset]

Can you define what do you mean by large scale? ... How many light years is considered large scale? ...What do you mean by tiny inhomogeneities? ... How many lightyears is considered tiny?

Quantum I think you raised a valid question. The principles of Isotropy and Homogeneity are invoked on a regular basis, independent of any mention of a specific numerical scale. Maybe it would be useful to start at some specific numerical extremes and work our way toward the muddled middle.

(For the sake of discussion let's adhere our own frame of reference at this point in space-time, rather than reconstructing what we think the universe looks like from another perspective such as at the edge of the void or 100 billion years into a hypothetical future.)

Assume an observable universe from our current perspective of 13 billion light year radius, giving a volume of 9.2 trillion cubic light years.

If the void had been discovered to be a sphere with a radius of 9 billion light years, it would occupy 1/3rd of the volume of the entire observable universe. I would venture to say that that would violate isotropy and homogeneity assumptions.

(Even then, I am out on a limb. I am ignoring the portion of the universe outside our observable horizon.)

If the void were instead 5 billion light years in radius, it would occupy only 5% of the universe, so I would venture to claim that isotropy and homogeneity would be preserved.

The actual void only occupies 5/1000 of 1%. That's one tiny pothole.

The link in Nereid's post to the Millennium Simulation shows beautiful images of the fine, lattice-like structure matter distributed over billions of light years. Those images for me embody validity of the cosmological principle.

 

[russ_watters]

Depends on how big the dip is relative to your model of the road. The cosmological principle is never exactly true on any scale and so the FRW model will not be a perfect description of the universe. The observation of an unusually large void might suggest that the FRW model is not quite as good an approximation as we might have thought on scales comparable to the void's size, but it certainly doesn't invalidate the Big Bang.

The real issue is whether or not inflation could explain such a large void, since it claims to predict the initial spectrum of fluctuations. The vast majority of observations done so far support gaussian random phase initial conditions, as predicted by inflation. If it could be shown that the distribution of matter is inconsistent with these initial conditions, then it might bring inflation into question, but it's hard for me to see how it could challenge the Big Bang framework.

I've never simulated anything quite so complex, but it is worth noting that for some systems, small changes in the initial conditions can produce large differences in the resulting simulations. I suspect these models work the same way so if, in fact, the void is larger than the simulations would predict, the actual error in the model's starting parameters could still be quite small.

And as sysreset noted, even if that pothole turns out to be a lot larger than predicted, it is still one tiny pothole.

 

[SpaceTiger]

I've never simulated anything quite so complex, but it is worth noting that for some systems, small changes in the initial conditions can produce large differences in the resulting simulations. I suspect these models work the same way so if, in fact, the void is larger than the simulations would predict, the actual error in the model's starting parameters could still be quite small.

The location and amplitude of large-scale voids should be easily traceable to the post-inflation perturbation spectrum. The growth of structure is still approximately linear (meaning it's still governed by linear differential equations) on scales comparable to the claimed size of this void, so you wouldn't expect any extreme sensitivity to initial conditions. You would, however, see such sensitivity in the positions of galaxies near clusters (for example).

And as sysreset noted, even if that pothole turns out to be a lot larger than predicted, it is still one tiny pothole.

He's right in that the supposed void wouldn't be evidence against the Big Bang. It would, however, be difficult to explain it with gaussian random phase initial conditions and what we currently think is the amplitude of the power spectrum. I think it's far more likely that their estimate of the void's size is just wrong and that the "extreme" CMB cold spot can be explained by a combination of effects at the surface of last scattering and at intermediate redshifts. This explanation would be ad hoc if it weren't for the a posteriori nature of the analysis on the cold spot.

 

[quantum123]

Fine, the pothole is 0.001% of the observable universe.
So you think it is small.
But some people think that it is big enough to be a sign that another alternate universe exists.
So is the pothole big or small?

 

[Nereid]

Local Void vs Dark Energy: Confrontation with WMAP and Type Ia Supernovae - a recent preprint (http://arxiv.org/abs/0712.0370" ) might be of interest to you quantum123 (and other readers) - it presents a 'minimal void' model, in which we are located inside a void (region underdense by ~40%) of several hundred million light-years in radius, and asks how well such a model fits the relevant cosmological observations.

The answer the authors give is, 'rather well'! (Of course, it's just a preprint at this stage)

Of particular interest may be the range of observations they consider: not only the high-z Ia SNe (high redshift type Ia supernovae) and the Year 3 WMAP observations of the CMB, but also BBN observations (primordial abundance of light nuclides), BAO observations (baryon acoustic oscillations - a peak observed in the galaxy-galaxy correlation function of LRGs), observations from large-scale structure and weak lensing, and ISW correlations (integrated Sachs-Wolfe effect)!

This also points to something Space Tiger mentioned: relating the observed CMB 'extreme' cold-spot to only one cosmological parameter is not so clean at this stage - Alexander et al. do also look at a couple of additional 'tweaks' (and mention that at least one class of 'alternative universe' models is a poor fit) ...

Oh, and the 'pothole' is very, very small quantum123 ... it just happens to be, apparently, the biggest pothole we've found so far ...

 

[Chris Hillman]

it is worth noting that for some systems, small changes in the initial conditions can produce large differences in the resulting simulations. I suspect these models work the same way so if, in fact, the void is larger than the simulations would predict, the actual error in the model's starting parameters could still be quite small.

Just wanted to point out that the question of stability in cosmological models (including but not limited to ones which undergraduate students of gtr are likely to encounter) has been extensively studied using the methods of dynamical systems; see for example Dynamical Systems in Cosmology, J. Wainwright and G. F. R. Ellis (editors), Cambridge University Press, 1997. Notice this typically involves reducing a complicated nonlinear PDE (the EFE) to a system of nonlinear ODEs.

(For those who have no idea what "stability" means in this context, suppose we consider an exact solution which is a perturbation of an FRW model and imagine that we have a slicing which approximates a homogeneous isotropic Riemannian three-manifold at some "time". Then, roughly speaking, we can ask whether initially perturbations grow larger as "time" progress? Or as we run time backwards?)

Thanks to all the mentors who showed up to help!

 

[Nereid]

One more thing on the difference between a big void (if that's what the extreme CMB cold spot turns out to be) and a 'pothole': contrary to the impression you may get reading some of the popular press articles, 'voids' are not empty ... they are simply regions in which the average density is (significantly, somewhat, ...) lower than the universal average.

For example, the Boötes void - the largest (?) before the CMB extreme cold spot was discovered - is certainly (very) under-dense, but it is also certainly not empty! For example, http://adsabs.harvard.edu/abs/1996AJ...111.2141S", a paper published in 1996, reported the discovery of many new galaxies in the small part of the void the authors studied; I think the number of known Boötes void galaxies is over 50. Also, given that some of these galaxies have AGNs, that some are undergoing mergers or other interactions (or have done so), and that many stars have gone supernova there, the medium between the galaxies in the void will certainly contain gas, dust, 'rogue' stars, planetary nebulae, ... and maybe even some dwarf galaxies.

 

[Garth]

And a cosmologist living on a planet in the middle of the Bootes void, who compared the Hubble flow of nearby galaxies with those further away, would conclude the universe was accelerating...

Local Void vs Dark Energy: Confrontation with WMAP and Type Ia Supernovae

It is now a known fact that if we happen to be living in the middle of a large underdense region, then we will observe an ``apparent acceleration'', even when any form of dark energy is absent.

Garth

 

[Nereid]

And a cosmologist living on a planet in the middle of the Bootes void, who compared the Hubble flow of nearby galaxies with those further away, would conclude the universe was accelerating...

Local Void vs Dark Energy: Confrontation with WMAP and Type Ia Supernovae

Garth

Hmm ... I seem to recall that someone else cited that preprint, earlier in this thread, ... I wonder who?

 

[Garth]

Yes, I wonder!

It just shows you that great minds think alike and fools seldom differ!

The point of me citing that link was, of course, that the hypothesis of us being in a relative void need not be too much of a violation of the Copernican Principle.

Garth

 

[quantum123]

Would a doorway to another universe mean that the cosmological principle is incorrect?

 

[Garth]

The point of me citing that link was, of course, that the hypothesis of us being in a relative void need not be too much of a violation of the Copernican Principle.

Another revision of Professor Sarkar's paper, which has now been accepted for publication in a special issue of General Relativity and Gravitation, Is the evidence for dark energy secure?.

This paper makes the point that:

The precision CMB data can be equally well fitted without dark energy if the spectrum of primordial density fluctuations is not quite scale-free and if the Hubble constant is lower globally than its locally measured value. The LSS data can also be satisfactorily fitted if there is a small component of hot dark matter, as would be provided by neutrinos of mass 0.5 eV. Although such an Einstein-de Sitter model cannot explain the SNe Ia Hubble diagram or the position of the `baryon acoustic oscillation' peak in the autocorrelation function of galaxies, it may be possible to do so e.g. in an inhomogeneous Lemaitre-Tolman-Bondi cosmology where we are located in a void which is expanding faster than the average.

It remarks:

Such alternatives may seem contrived but this must be weighed against our lack of any fundamental understanding of the inferred tiny energy scale of the dark energy. It may well be an artifact of an oversimplified cosmological model, rather than having physical reality.

So might it be the case that the Copernican Principle does not apply to our position in space and instead we are in a 'special' place, i.e. in a void?

If we see other voids, such as those in Bootes and the WMAP Cold Spot, then this hypothesis may not be so "contrived" after all.

And yes quantum123 the Cosmological Principle would still apply to the universe on the largest scales, even if the void 'pothole' is a "doorway to another universe", but if Sarkar's hypothesis is correct then it would not apply to the 'immediate' region around our Local Group.

Garth

 

[pervect]

If you were to look at Mt Everest, would you say that the figure of the Earth is not an ellipsoid because the mountain is so tall? Or would you say that the Earth is essentially an ellipsoid, because the mountain is so small?

 

[fasterthanjoao]

Would a doorway to another universe mean that the cosmological principle is incorrect?

I think, as has been shown by a good people already, you are misunderstanding and mixing priorities. Paraphrasing the same question and point doesn't help! It would be useful to know to what level you have studied physics: the issue of homogeneity and isotropy is only assumed as a starting point. Physics at any level needs to take a starting set of assumptions, and gradually perturb your model until the results match observation.

The FRW model (as you will find when you actually start studying cosmology) is not only a very nice starting point but does yeild some useful results, even if the finer points aren't accurate. To say that the model is worthless because absolute homogeneity and isotropy are not observed is naive, I'm sure you will know if you have studied chemistry at any level the value of the Bohr model of the atom - to a certain level results can be useful in making predictions, even though the fundamental essence of the model is 'wrong' (more correct to say that it has been replaced in mainstream physics by a quantum model).