Is the Universe Really Expanding?

[George Jones]

Could someone please explain to me how exactly this independent measurement was inferred from the WMAP data?

Curvature causes distortions in the small temperature anisotropies present in the backgorund radiation. The sizes of the anisotropies seen indicate that the universe is (very close to being) spatially flat (I don't know the details of the calculation), which requires that the matter/energy density of the universe by very close to the critical value. Even when dark matter is taken into account, we can only get a density of about 25-30% the critical value.

The supernova data indicates that dark energy/cosmological constant is responsible for a density of about 70-75% of the critical density.

These two results strongly reinforce each other.

 

[oldman]

Curvature causes distortions in the small temperature anisotropies present in the backgorund radiation. The sizes of the anisotropies seen indicate that the universe is (very close to being) spatially flat (I don't know the details of the calculation), which requires that the matter/energy density of the universe by very close to the critical value. Even when dark matter is taken into account, we can only get a density of about 25-30% the critical value.

The supernova data indicates that dark energy/cosmological constant is responsible for a density of about 70-75% of the critical density.

These two results strongly reinforce each other.

George, thanks for your prompt reply. Your post clarifies my understanding of this aspect of the WMAP results, which now runs along the following lines (please correct me --- I've probably got it wrong):

1. The first peak in the angular power spectrum of the CMB temperature fluctuations is caused by changes in the metric that occur while the CMB radiation is crossing overdense regions of the (almost homogeneous and isotropic) universe, en route to us.

2. The position of this peak depends on the spatial geometry of the universe. Its measured position shows that this geometry is very nearly Euclidean. In the context of a FRW model, Euclidean geometry fixes the total density of mass/energy in the universe (given the measured value of the Hubble constant) at the so-called critical density.

3. The total mass and energy density of the universe measured from luminosity ratios (visible matter) and gravitational effects (galaxy rotation curves, virialised cluster-galaxy speeds) is only about 25% of this critical density.

4. The resultant density deficit (of about 75% of the critical value) agrees with the deficit required to account for small deviations from linearity of the upper end of the Hubble plot, deduced from the use of type 1a supernovae as standard candles. The deficit is assumed to be made up of "dark energy", which, as noted in post #82 of this forum, is:

...one of the most puzzling aspects of modern cosmology and I think it would be naive of us to claim that we really understand what's going on here. Astronomers are working overtime to understand and quantify its effects, but we would still like a physical understanding of the mechanism that gives the vacuum energy. Is it the zero-point energy of QFTs? Is it a scalar field? Is it some exotic kind of particle? I'm happy to say that we still don't know and there is still much to be learned from our universe.

 

[SpaceTiger]

1. The first peak in the angular power spectrum of the CMB temperature fluctuations is caused by changes in the metric that occur while the CMB radiation is crossing overdense regions of the (almost homogeneous and isotropic) universe, en route to us.

All of the peaks in the angular power spectrum are fluctuations in the gas that emitted the radiation and don't come into being en route. These are called primary anisotropies and are created by the sound waves at the surface of last scattering. Some of the weaker anisotropies are created during the voyage of the radiation between z=1100 and z=0 and are called secondary anisotropies.

The rest of your points are correct.

 

[oldman]

All of the peaks in the angular power spectrum are fluctuations in the gas that emitted the radiation and don't come into being en route. These are called primary anisotropies and are created by the sound waves at the surface of last scattering. Some of the weaker anisotropies are created during the voyage of the radiation between z=1100 and z=0 and are called secondary anisotropies.

The rest of your points are correct.

Thanks for clearing up my confusion with the Sachs-Wolfe effect, which I had thought was involved.

 

[SpaceTiger]

Thanks for clearing up my confusion with the Sachs-Wolfe effect, which I had thought was involved.

The Sachs-Wolfe effect is involved, in fact, but note that it is the non-integrated Sachs-Wolfe effect. The acoustic peaks are imprinted at the surface of last scattering, at which time the emitted photons must climb out of the potential wells from which they were emitted. In contrast, the Integrated Sachs-Wolfe (ISW) effect occurs as the photons pass through potential wells en route to our telescopes. The non-integrated variant is a primary anisotropy and the integrated variant is secondary.

 

[oldman]

The Sachs-Wolfe effect is involved, in fact, but note that it is the non-integrated Sachs-Wolfe effect ..... The non-integrated variant is a primary anisotropy and the integrated variant is secondary.

I've been struggling somewhat to understand the WMAP results. I suspect that there is a screen of computer modelling with sophisticated codes between basic physics that I can grasp and the remarkable conclusions of the mission.

Thanks again for this further clarification. It's most helpful. I have one further confusion, though, of a general nature, which I hope you can remove for me:

It has to do with one of the purposes served by the inflationary "scenario", namely to explain why the sky and in particular the CMB is so uniform on large angular scales --- i.e to solve the horizon problem by suggesting that the observable universe is an inflated fragment of a thermalised portion of the primeval universe.

If this is so, why are the most prominent temperature fluctuations seen by WMAP (namely those of the first peak in in the power spectrum) deemed only to be of linear dimensions of order 1/(H at last scattering)?

Should inflation not have amplified many primeval fluctuations to dimensions greater than 1/(H at last scattering), just as it is supposed to have amplified "thermalised uniformity" to cover the whole sky?

So my difficulty boils down to: why are large-scale temperature fluctuations not more prominent in the WMAP results?

 

[oldman]

Garth: in asking some questions later in this thread (my posts 90 and 96) I had missed these comments of yours. The first answers the query I raised in #90 (now resolved by Space Tiger). The second seems to involve a similar difficulty (my emphasis) that I describe in #96.

My apologies for not referring to your comments.

The need for the WMAP data to have DE arises because its constraints on all matter density are no more than 30% closure density (best estimate 27%) and the peaks in the power spectrum of the WMAP anisotropies are consistent with flat space that requires 100% closure density, therefore something is required to fill the gap and DE fits nicely...

The peaks of the WMAP power spectrum are all in the correct place for flat, or conformally flat space, but the large scale low-l mode fluctuations appear to be genuinely deficient, which is not consistent with infinite flat space. However, these two observations, first peak at ~ 1⁰ plus a deficient quadrupole, could be explained by a finite conformally flat universe.

This conclusion is not easy to reconcile with the standard theory but it might be just what the data is telling us.

Garth

 

[Chronos]

Oldman, 'h' does not change in the inflationary scenario so far as I know. It remains a universal constant tied to 'c'. Of course that implies 'c' is more fundamental than 'h'. Is that the essence of your question?

 

[oldman]

Oldman, 'h' does not change in the inflationary scenario so far as I know. It remains a universal constant tied to 'c'. Of course that implies 'c' is more fundamental than 'h'. Is that the essence of your question?

Chronos: thanks for your reply. It's not quite the question I was asking --- perhaps I foolishly confused the issue by talking about H. Let me rephrase my difficulty.

I'm concerned that inflation seems to conflict with the WMAP results in one important respect.

It is this: if one relies on inflation to spread "uniformity" over our sky (so as to resolve the horizon problem), one should expect inflation to also spread large-scale thermal irregularities. My understanding is that both thermal uniformity and tiny quantum fluctuations on all scales are postulated to be characteristic of the pre-inflation universe. It seems to me that when inflated, both should become features of the present observable universe.

But, as Garth pointed out, the WMAP results show that "the large scale low-l mode fluctuations appear to be genuinely deficient" .

I would like to know how one can "have one's cake" (solve the horizon problem) and at the same time "eat it" (accept the deficiency in low-l modes).

 

[hellfire]

My understanding is that both thermal uniformity and tiny quantum fluctuations on all scales are postulated to be characteristic of the pre-inflation universe.

Quantum fluctuations arise during inflation and their spectrum contains all wavelenghts. Modes at short wavelengths are strongly redshifted by the inflationary expansion of space so that their wavelength becomes larger than the horizon. Beyond the horizon at long wavelengths, the modes freeze out to a nonzero values of the amplitude. Later on, after inflation, frozen modes with equal wavelength reenter the horizon at the same time perturbing the distribution of the energy density.

This perturbations lead to the oscillatory behaviour of the plasma before of recombination. The plasma stops oscillating after recombination. The latest modes that reenter the horizon at the time before of recombination have a wavelenght of the size of the horizon at that time. At the time of last scattering the mode which enters the horizon at that time will lead to maximum fluctuations (first peak), and some modes that have entered before will produce standing waves with nodes at the edges of the horizon (other peaks).

Regarding thermal uniformity, the theory of inflation can be formulated in a way that a homogeneous distribution of energy density is available in any case, even if the initial conditions are not homogeneous.

 

[Mad_Morlock]

hypersphere key

I'm not sure this will be well recieved, but I had an idea regarding the topology of the universe that might do well as a model...

[edited non-mainstream theory]

 

[Wallace]

But Mad Morlock where is the evidence for your idea? What does it predict that improves upon the predictions of the current model? The universe, on current evidence is going to continue to expand at an accelerated rate henceforth (though extrapolation is always risky, particularly as we really have no idea about the physics of dark energy).

You are right about one thing though, your post is unlikely to be well received

 

[oldman]

Beyond the horizon at long wavelengths, the modes freeze out to a nonzero values of the amplitude. Later on, after inflation, frozen modes with equal wavelength reenter the horizon at the same time perturbing the distribution of the energy density...

Thanks for trying to educate me, Hellfire, but I'm not as smart as you give me credit for, and I lost you about here. I still fear that there's a conflict between the WMAP results and the resolution of the horizon problem...

 

[Chronos]

No conflict if you accept the LCDM model. It handily describes the observational results. It is a very good model that explains many things. Hellfire gave the basics for formulating a theory that preserves the assumptions without tossing out the baby.

 

[hellfire]

Thanks for trying to educate me, Hellfire, but I'm not as smart as you give me credit for, and I lost you about here. I still fear that there's a conflict between the WMAP results and the resolution of the horizon problem...

Do you agree that inflation solves the homogeneity problem (or horizon problem) regardles of the initial conditions? Inflation was formulated to solve this problem. Providing homogeneity, it was clear that the theory had to provide a mechanism to account for the small inhomogeneities in the CMB that are the seeds of the matter structures. It was some time later when it was realized that this mechanism could be quantum fluctuations during inflation.

I recommed to read the following article by Alan Guth:

Inflation and Cosmological Perturbations
http://arxiv.org/abs/astro-ph/0306275

It contains a brilliant narration of the historical steps for the formulation of this mechanism and it describes also some technical aspects.

 

[oldman]

the LCDM model... handily describes the observational results. It is a very good model that explains many things.

I'm certainly not disputing this kind of general statement, Chronos, but the devil is always in the details! My original query was about one detail, namely:

my difficulty boils down to: why are large-scale temperature fluctuations not more prominent in the WMAP results?

and in a following post:

I would like to know how one can "have one's cake" (solve the horizon problem) and at the same time "eat it" (accept the deficiency in low-l modes).

.

These quotes should also make it clear that I do agree with Hellfire

... that inflation solves the homogeneity problem (or horizon problem) (and that)... the theory ... provide(s) a mechanism to account for the small inhomogeneities in the CMB that are the seeds of the matter structures...this mechanism could be quantum fluctuations during inflation.

But nether of you have yet mentioned the deficiency in low - l modes, which the WMAP results now seem to show are real. This conflict is what bothers me. Or am I tilting at windmills?

I hadn't seen the 2003 paper by Guth that Hellfire kindly referred me to. I've glanced at it now, and it seems to complement his 1997 book (which I have)excellently. Thanks for the reference, Hellfire.

 

[SpaceTiger]

But nether of you have yet mentioned the deficiency in low - l modes, which the WMAP results now seem to show are real. This conflict is what bothers me. Or am I tilting at windmills?

There is a deficiency in the low-l modes, but it's only a relative deficiency...they still expected much less power on those scales than at the scale of the acoustic peak. The interpretation of this deficiency is still a matter of some debate. Some believe it is a sign of a non-trivial topological structure for the universe, some a signature of modified gravity, and some just a statistical fluke exaggerated by a posteriori statistics. Only time will tell.

 

[Garth]

(Edit: Crossed with ST's post.)

Not many low-l mode anisotropies are to be expected in the first instance, as they are the 'large' ones. Even so there are fewer than predicted by the LCDM model, is this perhaps just a statistical fluke?

It could be, however if the 'Axis of Evil' is removed as being some kind of local contamination then the chance that the remaining increased deficiency at the low-l modes be a statistical fluke becomes vanishing small.

Perhaps the Axis of Evil is indeed real and part of the cosmological structure of the CBM? In which case its alignment with local geometry is an 'a posteri' recognised statistical chance event and not significant. And the low-l mode deficiency may be disregarded as statistically insignificant.

However, one explanation for the deficiency may be that although the universe's spatial geometry appears flat and therefore the universe is infinite or very large compared with our horizons, it is in fact smaller so there was not enough room for the deficiencies to grow in the early, pre-Surface of Last Scattering universe but also spatially conformally flat. This, however, would require a modification of the theory by which the CMB data is analysed, i.e. it would require a modification of GR.

Garth

 

[oldman]

... The interpretation of this deficiency is still a matter of some debate ...Only time will tell.

That satisfies my curiosity. I hope that not too much time will pass before all becomes cut and dried. Thanks.

 

[oldman]

... one explanation for the deficiency may be that although the universe's spatial geometry appears flat and therefore the universe is infinite or very large compared with our horizons, it is in fact smaller so there was not enough room for the deficiencies to grow ...

I'm slightly puzzled by this suggestion, because the uniformity of the universe is postulated to have been grown by inflation to encompass the whole observed universe, thus solving the horizon problem. If there was room for this (call it l = 0?) mode to grow, why not room for low-l modes? But I don't trust my reasoning , and accept that others will probably resolve this anomaly in time.

If it were to "require a modification of the theory by which the CMB data is analysed, i.e. and ... a modification of GR", as you mention, the interpretation of much else might also change --- a welcome astonishment for a somewhat sceptical spectator like myself.

Thank you for your interest.

Garth[/QUOTE]

 

[Chronos]

I feel the non-trivial topology hypothesis has legs. The persistent redshift anomalies certainly suggest this possibility. In a finite universe, this [IMO] is a very plausible explanation - there may be quantum fluctuations embedded in the inflationary phase that produce localized variations in H0. I would be fascinated by any study that examines this possibility. I have toyed with this idea using LEDA and VizieR data and cannot rule it out.

 

[Garth]

Might the explanation of the low-l mode deficiency and apparent alignment be explained by an exotic topology? CMB Alignment in Multi-Connected Universes Not yet apparently!

We have investigated the question whether the strange alignment observed in low CMB multipoles can be explained by multi-connected space forms. There are several examples of such spaces which can explain the missing anisotropy power at large angular scales as measured by the temperature correlation function C(ϑ), ϑ > 60◦, or the angular power spectrum C_l for l = 2, 3. It is thus natural to ask for the alignment properties in such spaces.

......

But in no case we have found a model, where a significant fraction of the simulations possesses the alignment observed in the CMB sky. It remains to be seen whether there are other space forms which can more easily explain the alignment than the space forms considered in this paper.

Garth

 

[heusdens]

With all the crazy ideas that get thrown around in this forum, I thought it would be good to step back and review the mainstream view on cosmology in 2005. The field is advancing very rapidly, so it's possible that even the most reliable websites will be woefully out of date, both in terms of results and the evidence for them. Let's review, starting from the most secure and ending with the most puzzling/dubious aspects of the standard theories. I'll do this over the course of multiple posts, and feel free to interject and discuss at any point. Note that we are discussing mainstream cosmology, so this is not the place to present your favorite non-standard model for the universe. However, please do feel free to discuss observational evidence (or the lack thereof) for the standard theories.


1) Expansion

The universe is, without a doubt, expanding. The most striking evidence for this is the fact that nearly every object in the sky exhibits a redshift in the spectrum of light that is emitted from it. Furthermore, more distant objects are observed to have larger redshifts, exactly what you would expect for expansion. Alternative theories (such as Zwicky's "tired light hypothesis") were put forth and seriously considered in the first half of the 20th century, but have produced no correct predictions, nor are they consistent with any known physics. They have not been seriously considered by the mainstream for quite some time.

It should be noted that redshift is not the only reason we think the universe is expanding, but it was certainly the first evidence. Since the discovery of Hubble's Law in 1929, many more things have been deduced under the assumption of expansion (most notably, the Big Bang Theory) that also produce testable predictions. The success of these theories can be viewed retroactively as evidence for the expanding universe.


2) The Big Bang Theory

There is a lot of confusion amongst the general public about what the Big Bang Theory is really saying and which aspects of it are taken as gospel truth by the scientific community. In its simplest form, you can think of the argument as follows:

"If space is expanding and the universe has a finite size, then it must have been much smaller in the past".

How much smaller? Well, the standard assumption is that the universe had a creation event and expanded from a singularity to its present size[/color]. Such a distant extrapolation can't possibly be verified by the current observations, but we can safely say that the universe expanded from a much smaller size than its current one. There is good observational evidence for an epoch of nucleosynthesis approximately one minute after the creation event (z ~ 10⁸). Physical models of the conditions in this early phase of the universe were able to predict the relative abundances of the light isotopes (including hydrogen, helium, and deuterium) to very high accuracy.

There is even stronger evidence for recombination, an event that occurred when the scales in the universe were a 1000 times smaller than today (~400,000 years after the big bang). Recombination is what gives rise to the cosmic microwave background (CMB) radiation, a nearly blackbody spectrum that can also be modeled very accurately. The models are so accurate, in fact, that they have also allowed us to precisely measure some of the parameters of our universe. More on this later.

In addition, there is increasing evidence for an epoch of inflation, thought to occur 10^-35 seconds after the creation event, during which the universe may have expanded by as much as a factor of 10⁵⁰! If we could observationally confirm such a hypothesis, it would be an overwhelming success for both the Big Bang Theory and the scientific method itself. I'll also discuss the evidence for this in more detail later. There are a lot of nice websites on the Big Bang Theory (see here, for example), so web surf if you want to know more.

I agree on general on this outline of BB theory, except for the stuff marked in red. Although it can be theoretized that the theory of GR shows a singularity at the beginning, it is not mainstream scientific or part of the BB theory to claim that the singularity actually "happened", because it would mean that there was a moment in time at which time began (there was no time prior to it). But we don't know that at all, it is NOT a scientific fact!
What we can talk about and back up with observational evidence goes back to the origin of the CMBR, and theoretically we can go back to the Planck time. What happened before the Planck time we can not predict with current scientific theories (GR and QM), unless there is a theory of quantum gravity, and although some scientific theories have emerged here, to my knowledge there is not yet an accepted theory there.
What we can NOT talk about, scientifically, is talking about the actual singularity as a real event (happenening in space and time), since the very theory that comes up with it, is known to break down there, so it ain't scientific to say that there was a singularity at the begin, or to even suggest that there could have been a begin. (*)
So the singulairy is only a fictional point which boils up in models, but is not a scientific fact that this singularity actually exist. It would have contained infinite density for instance.
As a model for the early universe, the theory of inflation has been the most succesfull over the last couple of 20 years, and it has been shown that:

• inflation can start at in fact chaotic conditions (which means, not requiring special conditions for the early universe)
• once started, inflation could go on forever, although for every worldline, the period of inflation is finite. [compare that with a wildfire, every tree just burns for some specific time, but the fire itself can go on forever, at least theoretically; in a theoretically infinite universe, inflation could go on forever].
• there is no need for inflation to have begun at some time, it could have been past eternal.

(*)
And as a remark, from a philosophical point of view, it is necessary to acknowledge that as such the universe can not have a begin, as the universe contains all there is, since if there was, the universe would have needed to start out from nothing. But a nothing is only nothing, not a begin of even an infinitisimal small something. A nothing is merely a pure concept of thought, and not a concept that applies to physical reality. Don't interchange that with a vacuum (the absence of ordinary matter), since a vacuum definitely contains something (energy, fields, spacetime metric, etc.)

 

[hellfire]

SpaceTiger's claim is correct if you take singularity = an event or a location at which general relativity and the classical notion of space-time break down.

 

[Chronos]

A universe from 'nothing' is not as far fetched as it may sound. Under the laws of thermodynamics, it is virtually required. Entropy is illogical in an infinitely old universe that includes causality.

 

[heusdens]

A universe from 'nothing' is not as far fetched as it may sound. Under the laws of thermodynamics, it is virtually required. Entropy is illogical in an infinitely old universe that includes causality.

That is not correct, if 'nothing' causally connects to any something, it is not 'nothing', but already a potential something.

You can't make up arbitrary physics law from nothing.

Qauntum mechanics for instance, is not applicable to 'nothing', because a 'nothing' is not part of any reality and has no physical description, it is just a concept of thought. If it would, then 'nothing' would not be 'nothing' but full of potential something.

And btw. this whole issue is outside the domain of physics, if there ain't a physical description of reality, there is no physician or physical law that can deal with it.

That one can not perceive of reality without contradictions somewhere, does not mean that reality does not exist, but that our way of describing it is incorrect.

The law of Thermodynamics (2nd law) is used over and over again to somehow 'proof' that the world would have needed a begin (a begin from 'nothing' !), but what one does not see is that the law of thermodynamics is not usefull in that context. It is restricted to finite systems only, which are not thermally connected to the rest of the universe.

The infinite universe is not a problem, since in any case, any timeline need to be strictly finite. The bottom line however is that one can not perceive of infinity without a contradiction.

 

[heusdens]

SpaceTiger's claim is correct if you take singularity = an event or a location at which general relativity and the classical notion of space-time break down.

Therefore, it is not an 'event'.

 

[hellfire]

Therefore, it is not an 'event'.

Ok, you may be right with the wording. What I was trying to point out is that the claim of SpaceTiger is correct, as long as you take the definition of singularity that is given within general relativity. This definition can be formulated in a very precise an formal way and there are singularity theorems that prove that the universe must have had such a singularity in its past. This is actually the mainstream view.

 

[Mike2]

The law of Thermodynamics (2nd law) is used over and over again to somehow 'proof' that the world would have needed a begin (a begin from 'nothing' !), but what one does not see is that the law of thermodynamics is not usefull in that context. It is restricted to finite systems only, which are not thermally connected to the rest of the universe.

The requirement of causality is that the next fact or event is materially implied by the previous condition. It is logically valid that a true conclusion can be implied by a falsehood, ie. 0->1 is logical. Thus the universe can come from nothing. Logic was developed from the most complete generalization of physical observations. One thing seemed to lead to another until we generalized the "one thing" as a premise and "another" as the consequences until now we accept that this is the way to think about anything. Now we are in the habit of assigning the property of being true to physical facts which do exist, and false to those supposed facts whcih really don't exist. We assign truth to existence and fasle to non-existence. So the very first fact would represent "True" materially implied by non-existence which is false. The first sample of existence completely distinguishes true from false. And the certainty of its existence is 100%. If anything at all is knowable with absolute certainty, it is that reality exists. What we can say about the universe after that would be less certain. And we can only decompose the absolute certaintly about the property of existence to other properites which are not as certain. So it seems probabilities would enter the calculations about subsystems of reality.

 

[heusdens]

The requirement of causality is that the next fact or event is materially implied by the previous condition. It is logically valid that a true conclusion can be implied by a falsehood, ie. 0->1 is logical. Thus the universe can come from nothing. Logic was developed from the most complete generalization of physical observations. One thing seemed to lead to another until we generalized the "one thing" as a premise and "another" as the consequences until now we accept that this is the way to think about anything. Now we are in the habit of assigning the property of being true to physical facts which do exist, and false to those supposed facts whcih really don't exist. We assign truth to existence and fasle to non-existence. So the very first fact would represent "True" materially implied by non-existence which is false. The first sample of existence completely distinguishes true from false. And the certainty of its existence is 100%. If anything at all is knowable with absolute certainty, it is that reality exists. What we can say about the universe after that would be less certain. And we can only decompose the absolute certaintly about the property of existence to other properites which are not as certain. So it seems probabilities would enter the calculations about subsystems of reality.

I don't think you're on the right track, because to begin with "false" has no meaning without "true". "False" and "true" are just opposites of each other, that belong to each other, and one can not exist without the other.
There is no dark without light. There is no nonbeing without being.

In other words those opposites (like false & true, light & dark, being & nonbeing) have no independend existence, but exist only in their unity of opposites.

Further, and as seen by dialectics, these union of opposites form a higher unity, so the unity of being & nonbeing is just becoming.

See for example Hegel, Science of Logic, Doctrine of Being:
http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm