Comparison of the Mainstream and the Self Creation Freely Coasting models

[selfAdjoint]

Thank you for that link, you may also be interested in Nina Byers Noether’s Discovery of the Deep Connection Between
Symmetries and Conservation Laws[/URL].

There were two questions left after the formulation of GR, treated separately: the local conservation of energy and the full inclusion of Mach's Principle. Emmy Noether dealt with energy-conservation early on and Brans and Dicke tried to deal with Mach's Principle in the 1960's.

SCC deals with both questions simultaneously.

The problem with the local conservation of energy is that the measurement of energy is frame dependent, in order to conserve energy you need to specify a frame of reference in which it is conserved, a preferred frame. I use Mach's Principle to select that frame.

The question of preferred frames in SCC is a deep one.
The field equations (Jordan frame) are manifested covariant, there are no preferred frames, although the matter field energy-momentum tensor is not conserved. (It is when conformally transformed into the Einstein frame). However if you select one particular fame, the 'Machian' Centre-of-Mass (Momentum) frame for the system in question then in that frame of reference energy is locally conserved.

I hope this helps.

Garth

I would call the Machian principle not a question, as if physics demanded it, but a philosophical preference. Einstein was a Machian at first but found his theory did not support it and was able to abandon it. I am not criticising SCC, just pointing out that there does not appear to be a crying need to build Mach into one's theories.

 

[Garth]

I would call the Machian principle not a question, as if physics demanded it, but a philosophical preference. Einstein was a Machian at first but found his theory did not support it and was able to abandon it. I am not criticising SCC, just pointing out that there does not appear to be a crying need to build Mach into one's theories.

Yes, selfAdjoint, thank you for that observation. I was using the word 'question' to mean 'the question of whether it should be included or not', it may even be emphasised by calling it a 'problem' instead.
The 'question' about Mach's Principle is closely related to the 'question', or 'problem' of the local conservation of energy. Quoting from my link above to that paper of Byers:

The failure of local energy conservation in the general theory was a problem that concerned people at that time, among them David Hilbert, Felix Klein, and Albert Einstein.
Energy conservation in the general theory has been perplexing many people for decades. In the early days, Hilbert wrote about this problem as ‘the failure of the energy theorem ’. In a correspondence with Klein [3], he asserted that this ‘failure’ is a characteristic feature of the general theory, and that instead of ‘proper energy theorems’ one had ‘improper energy theorems’ in such a theory. This conjecture was clarified, quantified and proved correct by Emmy Noether.

It is important to see the significance of this "failure of the energy theorem" in GR, for example:

In a laboratory on Earth (a 'supported frame of reference') you lift a stationary kilogram weight and put it on a shelf. Where has the energy used to lift it gone to? You have expended energy in lifting it and so your total energy, has gone down. Yet (in GR) the 'rest' mass of the weight has not altered, so where has the energy gone? The standard answer is "into the field".

In GR "there is transfer of energy to and from the gravitational field and it has no meaning to speak of a definite localization of the energy of the gravitational field in space...
At any given spacetime point one may choose a set of coordinates for which the gravitational fields vanish (g_uv reduces to the flat spacetime Minkowski metric and the Christoffel symbols vanish). This is guaranteed by the equivalence principle which states that one can always choose a coordinate system such that spacetime in the neighborhood of a given point is Minkowski (flat). Thus one may see why it is not meaningful to speak of a localized energy density for gravitational fields." " (Quoted from Byers' paper)

Thus, while it may seem that "there does not appear to be a crying need to build Mach into one's theories", is there a crying need to build in a local conservation of energy? That conservation requirement needs a frame of reference and that is why Mach is also required to select out such a 'preferred' frame.

The standard answer is to say there isn't a need for either, but the maverick in me has long suggested that in fact there is! As GPB is testing both theories at present we may not have to wait much longer to find out.

Garth

 

[Garth]

Age of the Universe

Next, from "Review of Mainstream Cosmology"

4) Age of the Universe
Firstly, there are globular clusters. From what we know about stellar evolution, we can model populations of stars and, under the assumption that they were all born at the same time, determine their age. When we do this with Milky Way globular clusters, we get an age of around 12 +- 3 billion years. Not technically a determination of the universe's age, but certainly a lower limit.

What about radioactive elements? Can we somehow use them to infer the age of the universe? It turns out that we can. Recent detections of Uranium-238 and Thorium-232 in stars have allowed us to use the traditional radioactive dating method to obtain an age of 12.5 +- 3 billion years. Again, a lower limit, but completely independent from and consistent with that from stars.

Finally, there are the measured cosmological parameters. When brought together and analyzed carefully, we can very tightly constrain the age of the universe to be 13.7 +- 0.2 billion years. It is very reassuring that this is consistent with both of the above ages. In fact, the standard model predicts that the Milky Way should have formed very early in the life of the universe, so the fact that the other two ages are of the same order (and not much less) is also consistent. One way to falsify the standard model would be to find something that is significantly older than 13.7 billion years. For a while, the globular cluster measurements were thought to represent such a falsification, but with the improvement of both our globular cluster measurements and our cosmological measurements, we are now finding nice agreement.

I thank ST for this clear exposition of the mainstream view.
It is important to note the age parameters, already posted, #2 on this thread, that have been determined by the standard interpretation of the WMAP data.
Hubble time, t_H is given by t_H = 10.2/h Gyrs.
where H = h.100 km/sec/Mpsc.
WMAP determines h = 0.72
so t_H = 14.2 Gys .

In a spatially flat, matter dominated dust Friedmann universe
R(t) = R₀(t/t₀)^2/3
and the present age of the universe = 2/3t_H = 9.44 Gyrs.

Thus the universe looks 'a bit young' for the components within it: i.e. the globular clusters and radioactive fossils. Furthermore, the universe would be even younger if the density or pressure were greater.

However all is not lost, acceleration in the past would have meant that the universe had been expanding more slowly in the ancient past and therefore is older than it at first seems today. This acceleration can be produced by inserting negative pressure into the Friedmann equations.

Therefore the observation that SN Ia in high red shift galaxies were fainter than expected was seized upon as a solution to two specific problems, as these observations provided evidence that the universe had accelerated in the past, if interpreted in the GR paradigm.
1. The universe 'is older than it looks' thereby resolving the age problem.
2. This negative pressure could be caused by Dark Energy that provided the extra cosmological density required for closure (Omega = 1).

But note that this DE has to be carefully modeled, in ST's words, "These things were invented to explain the data, not the other way around." (post #38 in "Mainstream" thread).

The mainstream model requires massive acceleration in the earliest universe - Inflation. However the expansion has to be that of a radiation dominated universe R(t) = R₀(t/t₀)^1/2 for BBN (primordial nucleosynthesis) to be correct. So DE is insignificant in this period, but then becomes significant in the 'dark ages' and early galactic age, but would appear to be insignificant again in the modern epoch otherwise we could detect it locally.

In comparison the Freely Coasting model, as produced by the SSC gravitational field equations, has a simple evolution R(t) = R₀(t/t₀) and the age of the universe is simply 14.2 Gys. The independently determined ages of its various components sits comfortably within this constraint, as do the formation of Pop III stars, quasars and the earliest galaxies.

There is no acceleration, no DE, and yet the model fits the distant SN Ia data, here, page 4 as recognised by Perlmutter here, page 24.

The middle solid curve is for (Omega M,Omega L) = (0,0). Note that this plot is practically identical to the magnitude residual plot for the best-fit unconstrained cosmology of Fit C, with(Omega M, Omega L) = (0.73,1.32).

Finally, as there is no requirement to make up the density closure because the total Omega = 0.33, why "multiply the entities" with the "invention" of DE?

Garth

 

[Kea]

In comparison the Freely Coasting model, as produced by the SSC gravitational field equations, has a simple evolution R(t) = R₀(t/t₀) and the age of the universe is simply 14.2 Gys.

Interestingly, this is similar to the age calculated by the recent Wiltshire Machian cosmology.

 

[Garth]

Interestingly, this is similar to the age calculated by the recent Wiltshire Machian cosmology.

That is interesting. Note that model also adds Mach to GR, and also finds it does not need DE to explain cosmological constraints. Does it have any specific falsifiable tests as SCC does?

Garth

 

[Kea]

Does it have any specific falsifiable tests as SCC does?

Hi Garth

Well, yes, but it's early days yet. An improved version should appear shortly. A reanalysis of WMAP data could take a long time. It really depends on whether or not an experimental group becomes interested in it, I guess.

Cheers
Kea

 

[Garth]

Interestingly, this is similar to the age calculated by the recent Wiltshire Machian cosmology.

Note also that Kolb (Edward W?) was the author of the original " A coasting cosmology " paper.
Perhaps there is an even closer relationship between the two theories.

Garth

 

[turbo]

Here are three lectures giving Rocky Kolb's thoughts on Dark Matter and Dark Energy. Given at SLAC August 2003. You may find his approach refreshing.

http://www-project.slac.stanford.edu/streaming-media/SSI/2003/ram/SSI_8_4am1.ram
http://www-project.slac.stanford.edu/streaming-media/SSI/2003/ram/SSI_8_5am1.ram
http://www-project.slac.stanford.edu/streaming-media/SSI/2003/ram/SSI_8_6am1.ram

 

[hellfire]

In comparison the Freely Coasting model, as produced by the SSC gravitational field equations, has a simple evolution R(t) = R₀(t/t₀) and the age of the universe is simply 14.2 Gys.

How do you calculate this? For a linearly expanding universe the age is equal to the inverse of the Hubble parameter and this yields 13.77 Gy.

 

[Garth]

How do you calculate this? For a linearly expanding universe the age is equal to the inverse of the Hubble parameter and this yields 13.77 Gy.

You are correct, thank you for spotting that.
I copied the wrong value, from where I cannot remember,
t_H = 10.2/h Gyrs. wrong!
in fact t_H = 9.78/h Gyrs.
where H = h.100 km/sec/Mpsc.

So if h = 0.72 then t_H = 13.6 Gyrs.

What value of h are you using?

All this means to my argument is that all my time values have to be adjusted by a factor 13.6/14.2 = 0.958. i.e. 5% less.

Garth

 

[hellfire]

What value of h are you using?

0.71, I had in mind this was the WMAP best fit value.

 

[Garth]

0.71, I had in mind this was the WMAP best fit value.

I don't think the second significant figure is very robust, but we do have a much better handle on Hubble time than previously - unless there is some systematic error.

...Like my value t_H = 10.2/h Gyrs; I've been wondering where I got this value from and remembered I did a 'back of an envelope' calculation at the beginning of this thread. I must have mistaken the reciprocal somewhere; 1.02 = 1/0.978...

Garth

 

[Garth]

Therefore, not wanting to be remembered on PF for a number of mistakes, , I here correct my post #2, however the basic arguments that depend on these numbers has not changed.

The look back time t_l as a function of red shift z is given by:
In GR
t_l/t_H = (2/3)(1 - 1/(1 + z)^3/2)
In SCC
t_l/t_H = (1 - 1/(1 + z))



With t_H = 9.78/h Gyrs.
Lets take the WMAP determination of h = 0.71 so t_H = 13.8 Gys.
and the age of the universe = 2/3t_H = 9.18 Gyrs. in GR.
(Note: acceleration since z = 6 can considerably increase this age of the universe without affecting the calculated durations from BB below).
And the age of the universe = 13.8 Gyrs. in SCC.

Using t_z=x to be the age of an object now observed at a red shift x, we have for time after BB:

For "re-combination" - the surface of last scattering of the CMB, z = 1000,
t_z=1000 = 206,000 yrs. in GR
t_z=1000 = 13.8 Myrs. in SCC

for the onset of metallicity, i.e. Pop III stars, z = 20
t_z=20 = 67.8 Myrs. in GR
t_z=20 = 657 Myrs. in SCC

for quasar 'ignition' z = 8
t_z=8 = 241 Myrs. in GR
t_z=8 = 1.53 Gyrs. in SCC

for 'modern' metallicity in Quasar SDSS J1030+0524 z = 6.28
t_z=6.28 = 332 Myrs. in GR
t_z=6.28 = 1.90 Gyrs. . in SCC.

The comparison shows that there is considerably more time for the development of Pop III stars, Quasars and early metallicity than in the mainstream model.

Garth

 

[Chronos]

Just to be fair to the mainstreamers, the vanilla GR prediction for the age of the universe [and look back time] is not generally accepted. Most would offer values closer to those obtained using Ned Wright's calculator:

http://www.astro.ucla.edu/~wright/CosmoCalc.html

Plugging in WMAP values yields these results:

Current age of universe: t = 13.67 Gy
z = 1000 t = 436,000 years
z = 20 t = 182 My
z = 8 t = 652 My
z = 6.28 t = 896 My

Also per WMAP, recombination occurred around z = 1089, which occurs at t = 378 My.

 

[Garth]

Just to be fair to the mainstreamers, the vanilla GR prediction for the age of the universe [and look back time] is not generally accepted. Most would offer values closer to those obtained using Ned Wright's calculator:

http://www.astro.ucla.edu/~wright/CosmoCalc.html

Plugging in WMAP values yields these results:

Current age of universe: t = 13.67 Gy
z = 1000 t = 436,000 years
z = 20 t = 182 My
z = 8 t = 652 My
z = 6.28 t = 896 My

Also per WMAP, recombination occurred around z = 1089, which occurs at t = 378 My.

Thank you for that Chronos as I said my numbers were based on the plain Einstein-de Sitter universe, a spatially flat dust filled model,
R(t) ~ t^2/3.
Acceleration extends my ages and that depends on the extent of the acceleration period and the equation of state used for Dark Energy. As neither of these two factors are known the result is very problematic. Is there another New Wright page where he shows the equations used in his 'calculator'?
Garth

 

[hellfire]

Is there another New Wright page where he shows the equations used in his 'calculator'?

You can check my cosmological calculator here. It is not as elaborated as Ned Wright ones, but the code is far simpler (cc_e.js). It is of free use, and if you have any questions about equations I can answer via PM. By the way, the age 13.67 Gly for the standard model follows from the assumption of 0.27 Omega matter, 0.73 Omega Lambda (w = -1) and h = 0.71.

 

[Garth]

You can check my cosmological calculator here. It is not as elaborated as Ned Wright ones, but the code is far simpler (cc_e.js). It is of free use, and if you have any questions about equations I can answer via PM. By the way, the age 13.67 Gly for the standard model follows from the assumption of 0.27 Omega matter, 0.73 Omega Lambda (w = -1) and h = 0.71.

Thank you hellfire,the standard model does seem to be clustering around those values.

The model would be more robust if we knew exactly what DE was. (if anything!)

The acceleration of the universe in the past depends on the equation of state of DE w = -1 relates to the cosmological constant, (hence 'Lambda' of LCDM), and false vacuum energy (ZPE anybody?), whereas w = -1/3 would be that of a string network, and w < -1 for 'quintessence'.

The model also requires the universe to be spatially flat, and therefore infinite, but where are the low mode anisotropies in the WMAP/BALLOON/COBE data? As I have pointed out on several occasions the data is also concordant with a conformally flat model such as a cone (freely coasting - SCC Einstein frame), or a cylinder (Einstein's original static model - SCC Jordan frame) or a torus. Any of these would be finite in size and able to explain the low mode deficiency in the CMB anisotropies.

Also note that the standard model critically depends on not only the interpretation of the WMAP data but also on that of the distant SN Ia luminosity data. That data is also concordant with the freely coasting model as in my link in post #33, here, page 4 and recognised by Perlmutter here, page 24.

The middle solid curve is for (Omega M,Omega L) = (0,0). Note that this plot is practically identical to the magnitude residual plot for the best-fit unconstrained cosmology of Fit C, with(Omega M, Omega L) = (0.73,1.32).

.

Comparing times from BB between the LCDM model as above and SCC we have:
Using t_z=x to be the age of an object now observed at a red shift x, we have for time after BB:

For "re-combination" - the surface of last scattering of the CMB, z = 1089,
t_z=1089 = 378,000 yrs. in GR
t_z=1089 = 12.7 Myrs. in SCC

for the onset of metallicity, i.e. Pop III stars, z = 20
t_z=20 = 182 Myrs. in GR
t_z=20 = 657 Myrs. in SCC

for quasar 'ignition' z = 8
t_z=8 = 652 Myrs. in GR
t_z=8 = 1.53 Gyrs. in SCC

for 'modern' metallicity in Quasar SDSS J1030+0524 z = 6.28
t_z=6.28 = 896 Myrs. in GR
t_z=6.28 = 1.90 Gyrs. . in SCC.

This comparison, using "Mainstream model" parameters, still shows that there is considerably more time for the development of Pop III stars, Quasars and early metallicity than in the mainstream model.

Garth

 

[Chronos]

The WMAP result suggesting reionization began around z = 20 is the tightest, and most model resistant constraint in current mainstream theory. The SCC limit is obviously more palatable. The other early events, such as rapid evolution of metallicity are not so troubling - at least to this point. Our weak understanding of stellar and galactic chemical evolution deserves much of the blame. But then again, it is not clear why reionization occurred at the pace it did [some would say too fast, some too slow]. The evolution of metallicity and reionization could easily be connected. The observations we need to resolve these, and other stubborn problems unfortunately reside in the cosmic 'dark ages' [z>6]. Some exciting projects are, however, in the works:

LOFAR
http://www.lofar.org/p/ast_sc_epoch.htm

Square Kilometer Array
http://www.skatelescope.org/pages/science_gen.htm

 

[Garth]

The WMAP result suggesting reionization began around z = 20 is the tightest, and most model resistant constraint in current mainstream theory. The SCC limit is obviously more palatable. The other early events, such as rapid evolution of metallicity are not so troubling - at least to this point. Our weak understanding of stellar and galactic chemical evolution deserves much of the blame. But then again, it is not clear why reionization occurred at the pace it did [some would say too fast, some too slow]. The evolution of metallicity and reionization could easily be connected. The observations we need to resolve these, and other stubborn problems unfortunately reside in the cosmic 'dark ages' [z>6]. Some exciting projects are, however, in the works:

LOFAR
http://www.lofar.org/p/ast_sc_epoch.htm

Square Kilometer Array
http://www.skatelescope.org/pages/science_gen.htm

Thank you for that. Yes the reionisation (even a very Extended reionization epoch) and metallicity are most probably connected - to Pop III stars, but how big and how many of them? If you have a few very large Pop IIIs then the ionisation will be patchy and metallicity likewise.

SCC would suggest that primordial metallicity and high primordial baryonic density (~22%) would allow many smaller Pop IIIs to form (100 - 1000 solar mass) that would produce a smoother ionisation pattern and distribution of metallicity than in the standard model. They would then leave behind IMBH's of that mass range constituting the DM today.

Is this too 'hand waving' a possibility?

Garth

 

[Chronos]

Everything is up for grabs until we have more and better observations of the hidden pieces of the puzzle. The tail end of the epoch of reionization is just within our observational grasp [the Gunn Peterson trough]. It currently looks like reionization will turn out to be a messy affair - something akin to starbursts in galactic evolution:

http://arxiv.org/abs/astro-ph/0411152
How Universal is the Gunn-Peterson Trough at z~6?: A Closer Look at the Quasar SDSS J1148+5251

http://arxiv.org/abs/astro-ph/0505065
Taxing the Rich: Recombinations and Bubble Growth During Reionization

 

[Garth]

From the paper A very extended reionization epoch ? the suggestion is that there was a late period of Pop III star re-ionisation that finished at z>=10.5. This would then date the end of such stars, the ‘transition red shift’.

However, in order that the photon flux does not violate the Lyman-α Gunn-Peterson optical depth constraints at z & 6, the PopIII star formation rate should start decreasing around z_trans ~ 11. This value of z_trans is marginally consistent with the observations of NIRB.

As a comparison therefore, the active lifetime of Pop III stars in the two models is calculated to be: (Using LCDM values for the GR model)

For the onset of metallicity, i.e. 'ignition' of Pop III stars, z = 20
t_z=20 = 182 Myrs. in GR
t_z=20 = 657 Myrs. in SCC

for the transition period, i.e. the end of Pop III stars, z = 10.5
t_z=10.5 = 450 Myrs. in GR
t_z=10.5 = 1.31 Gyrs. in SCC

Thus the active lifetime of Pop III stars is
268 Myrs in GR and 653 Myrs in SCC,
(alright, perhaps not to that accuracy!) i.e. over twice as long. Note that if this late re-ionisation period does not in fact exist then the transition period is much earlier and the Pop III lifetimes drastically reduced.

Two questions again; should this transition period be observable as a background of very early hyper-novas, and, in the SCC model, could these Pop III stars then leave behind the present DM in the form of IMBHs?

Garth

 

[Chronos]

Suspending disbelief, for the moment, the question becomes - can reionization be complete at z = 6 by the usual accounting system for the age of the universe [around 1 billion years after BB]? That seems to be a good question and frankly I don't have a good answer to that one. I will try to find one. You make my brain hurt sometimes.

 

[Garth]

Pop III stars are expected to be short lived; if they all formed from the 'same' post re-combination cosmological gas then they might be expected to burn themselves out within a short time more or less simultaneously and thus complete re-ionisation.

I see the difference between the two theories as being the primordial metallicity and baryonic density. The presence of significant primordial metallicity in SCC would allow smaller Pop III to form IMHO and the greater baryonic density would spawn far more of them. Thus re-ionisation and IGM metallicity could be more homogenous than in GR, and the present DM could consist of Pop III end products in the form of IMBHs ([10² - 10⁴]M_solar).

Garth

 

[Garth]

5) Flatness

Next from the "Review of Mainstream Cosmology" thread:

What do we mean when we say the universe is flat? Well, in short, we mean that the space can be described by normal Euclidean geometry; for example, the angles of a triangle add up to 180 degrees. In fact, the latter is exactly what we usually use in our attempts to determine flatness. One could actually go out and perform such an experiment by constructing a giant triangle (with, say, laser beams shooting from one mountain to another) and measure the angles of this giant triangle. If, within the uncertainties, the angles added up to 180 degrees, one would conclude that the space in that region was approximately flat. Of course, we know now that the space near the Earth's surface is very well approximated as flat, but there was no way for the ancients to be sure of this.

Likewise, without a direct measurement, there's no way that we can be sure whether or not the space in the observable universe is flat. This kind of thing is very difficult to do locally because we only expect the universe's curvature to be noticable on large scales (that is, at high redshift). It turns out the most effective method is to analyze the anisotropies in the cosmic microwave background (CMB), a last-scattering "surface" that was formed at around z ~ 1100 [For more information on the microwave background, see marlon's What is Cmb thread]. By looking at the length scale on which the CMB is most anisotropic, we can determine very precisely the flatness of the universe. Using WMAP, we were able to determine that the universe was flat to very high precision:

\Omega=1.02 \pm 0.02

For those not familiar with that notation, \Omega=1 is a flat universe. Buried in this notation, however, is an important assumption. What it really means is

\Omega=\frac{\bar{\rho}}{\rho_c}=\frac{8\pi G\bar{\rho}}{3H^2}

where \bar{\rho} is the average density of the universe and H is Hubble's constant. This is an elegant description of how mass curves space. That is, general relativity tells us that not only can we measure the geometry of space itself, but we can also infer its geometry by measuring how much mass and energy occupy it. This should be kept in mind when one considers that the total energy density of the universe has been measured to correspond approximately to that needed to flatten the universe. In other words, the pictures are consistent -- the geometry is flat and the contents are sufficient to flatten it.

In the following sections, I'll describe exactly what those contents are and how we measure their total contribution to the curvature of the universe.

Thank you again to ST for this clear exposition of the mainstream model.

The only evidence that the universe has closure, or near, closure density
\Omega_t=\frac{\bar{\rho}}{\rho_c}=\frac{8\pi G\bar{\rho}}{3H^2} = 1
is the analysis of the CMB data.

Every other measurement of density, galactic cluster velocity profiles, lensing etc, yield an average density of \Omega_m= 0.2 - 0.33.
The difference is attributed to Dark Energy in the mainstream model.

The observation of cosmological flatness is consequently very dependent on the CMB data, together, of course, with the natural predilection of the theory of inflation to that closure density. It is therefore important to see whether that is the only, or indeed the best interpretation of the CMB data.

The data consists of measurements of the angular size of CMB anisotropies which themselves arose from density fluctuations in the surface of last scattering. The angular sizes can be plotted against the depth of intensity fluctuations.
diagram here
Notice the good fit of the data at the first and subsequent peaks of the data points to the standard flat model line.

However, notice also the dropping away of the data points from that line at the largest angular scales.

This discrepancy is found also in the COBE and BALLOON data set and therefore seems to be a robust feature of the universe.

How can this be explained?

The standard flat model is infinite and these largest fluctuations should be present as predicted, on the other hand, if the universe were actually finite then such a deficiency at large angular scales would be expected as there would not be enough space in the early universe for these largest density fluctuations to exist.

Taking the low mode data points as well as the peaks it would be more accurate to describe the CMB anisotropy power spectrum as being consistent with a conformally flat and finite model.

Other plausible explanations of the discrepancy are being sought, however AFAIK none has been found.

The topology of a conformally flat and finite universe is modeled by either a cylinder or a cone. Draw a set of angles on a flat sheet of paper. That model represents the infinite flat mainstream model universe. Now roll the sheet into a cylinder, or cut out a sector and roll the sheet into a cone. In either case the angles do not change; conformal transformations preserve angles.

Therefore we can say that a conformally flat and finite model fits the WMAP data better than the mainstream infinite flat LCDM model.

SCC predicts a precise cosmological model, it is highly determined and therefore highly falsifiable. That prediction is of a static cylindrical model in its Jordan conformal frame and a freely coasting conical BB model in its Einstein conformal frame.

In either frame the model is conformally flat and finite. The SCC models are therefore more concordant with the WMAP data set than the mainstream LCDM model.

Garth

 

[Garth]

More about the low mode, large angle anisotropy deficiency: again diagram here ; taken from http://arxiv.org/PS_cache/astro-ph/pdf/0302/0302207.pdf page 29.

This discrepancy is found also in the COBE and BALLOON data set and therefore seems to be a robust feature of the universe.
How can this be explained?

Other plausible explanations of the discrepancy are being sought, however AFAIK none has been found.

What other explanations might there be?

The first is the shortfall does not actually exist but is simply a statistical quirk: The Statistical Significance of the Low CMB Mulitipoles

Some authors have argued that this discrepancy may require new physics. Yet the statistical significance of this result is not clear. Some authors have applied frequentist arguments and claim that the discrepancy would occur by chance about 1 time in 700 if the concordance model is correct. Other authors have used Bayesian arguments to claim that the data show marginal evidence for new physics. I investigate these confusing and apparently conflicting claims in this paper. I conclude that the WMAP results are consistent with the concordance LCDM model.

Whereas others have found a correlation with local geometry: Low-order multipole maps of CMB anisotropy derived from WMAP

We confirm the Tegmark et al. (2003) result that the octopole does indeed show structure in which its hot and cold spots are centred on a single plane in the sky, and show further that this is very stable with respect to the applied mask and foreground correction. The estimated quadrupole is much less stable showing non-negligible dependence on the Galactic foreground correction

which has been jumped on by the 'ban the BB' school.

What is to be made of this?

The standard interpretation is that of Efstathiou above, i.e. the discrepancy does not exist. However others disagree and in particular a possible correlation of the lowest modes with local geometry suggests it is real, but may have nothing to do with cosmology!

My suggestion?

In SCC the geometry is simple in the static Einstein conformal frame.

The universe has a scale size of \sqrt{12} H^{-1} and the surface of last scattering is at a distance of -H^{-1}ln(1+z), where z = 1028, so the universe at last scattering subtends 2 \pi \sqrt{12} /ln(1+z) rad across the sky. This is 3.14 rad or 179.6⁰, that is, the first mode.

Therefore SCC predicts that there should not be any anisotropy at mode one.

The inference is that the low mode WMAP data consists of two sources superimposed on each other, a local large angular scale effect with a signal of modes 1 -> ~10(?), and a CMB signal of a (conformally) flat universe that zeros at mode 1.


Is this plausible?

Note: One problem with this model is that such a angle subtended by the whole universe at recombination is that one would expect 'circles in the sky' in the WMAP data. These do not seem to exist.

Garth

 

[Garth]

In SCC the geometry is simple in the static Einstein conformal frame.

The universe has a scale size of \sqrt{12} H^{-1} and the surface of last scattering is at a distance of -H^{-1}ln(1+z), where z = 1028, so the universe at last scattering subtends 2 \pi \sqrt{12} /ln(1+z) rad across the sky. This is 3.14 rad or 179.6⁰, that is, the first mode.
......
Note: One problem with this model is that such a angle subtended by the whole universe at recombination is that one would expect 'circles in the sky' in the WMAP data. These do not seem to exist.

On the other hand ... Constraining the Topology of the Universe

The first year data from the Wilkinson Microwave Anisotropy Probe are used to place stringent constraints on the topology of the Universe. We search for pairs of circles on the sky with similar temperature patterns along each circle. We restrict the search to back-to-back circle pairs, and to nearly back-to-back circle pairs, as this covers the majority of the topologies that one might hope to detect in a nearly flat universe. We do not find any matched circles with radius greater than 25 degrees. For a wide class of models, the non-detection rules out the possibility that we live in a universe with topology scale smaller than 24 Gpc.

Note: The SCC 'circles in the sky' are ~180⁰ across (dipole). Are these worth looking for amongst the much deeper dipole mode caused by the Earth's motion relative to that surface of last scattering?

Garth

 

[Chronos]

Weird science

Thanks for relieving my headache, Garth. Your explanation remains tempting. But it is my duty to stick with the conservative view - dang it. Your questions are still too hard. Trust me, if I had a really good alternative, I would have already unloaded it on you. I like to think I have come up with a few, but nothing that blows it out of the water. Your arguments are sound, the math appears flawless... how annoying. I'm to the point I'm secretly rooting for GPB to affirm your 'wild' speculations.

 

[Garth]

I've been thinking hard about the 'circles in the sky', worried that their non-detection might be a 'stake in the heart' of SCC.

First my calculation above does not use the standard recombination z, correcting that, (yet again ), to z =1089 we obtain:

The universe has a scale size of \sqrt{12} H^{-1} and the surface of last scattering is at a distance of -H^{-1}ln(1+z), where z = 1089, so the universe at last scattering subtends
2 \pi \sqrt{12} /ln(1+z) rad = 2 \pi \sqrt{12} /ln(1090) rad across the sky. This is 3.11 rad or 178.3⁰, that is, still the first mode.

Therefore SCC predicts that there should not be any anisotropy at mode one.

However, I am pretty convinced that in a conformally flat universe with the topology the Jordan frame cylindrical model, there should be no circles in the sky at all. Instead the visible universe at that z, bounded by our light cone, is enlarged by a cosmological lensing effect across the whole sky. Or am I missing something?

Garth

 

[Chronos]

The only evidence that the universe has closure, or near, closure density is the analysis of the CMB data.

A point to consider. Supernova data can also be used to measure the curvature of the universe:
New Constraints on $\Omega_M$, $\Omega_\Lambda$, and w from an Independent Set of Eleven High-Redshift Supernovae Observed with HST
http://arxiv.org/abs/astro-ph/0309368

You may not want to give up on 'circles in the sky' just yet. This heavily cited paper is a good jumping off point for discussing the high angular CMB anisotropy: [edit]
The significance of the largest scale CMB fluctuations in WMAP
http://arxiv.org/abs/astro-ph/0307282

The jury is still out as to whether the universe is truly flat by these papers:

A Hint of Poincar\'e Dodecahedral Topology in the WMAP First Year Sky Map
http://arxiv.org/abs/astro-ph/0402608

Missing Lorenz-boosted Circles-in-the-sky
http://arxiv.org/abs/astro-ph/0403036

CMB Anisotropy of the Poincare Dodecahedron
http://arxiv.org/abs/astro-ph/0412569

The Shape of Space after WMAP data
http://arxiv.org/abs/astro-ph/0501189

Enjoy.

 

[Garth]

Thank you for those links.

A point to consider. Supernova data can also be used to measure the curvature of the universe:
New Constraints on $\Omega_M$, $\Omega_\Lambda$, and w from an Independent Set of Eleven High-Redshift Supernovae Observed with HST
http://arxiv.org/abs/astro-ph/0309368

The most important diagram in this analysis is Figure 6 on page 23 of that paper. Notice that they do not plot, for comparison, the empty universe \Omega_M=\Omega_\Lambda=0. This was plotted in the original paper by Permutter et al. as I posted above: here, page 24.

The middle solid curve is for (Omega M,Omega L) = (0,0). Note that this plot is practically identical to the magnitude residual plot for the best-fit unconstrained cosmology of Fit C, with(Omega M, Omega L) = (0.73,1.32).

So the evidence for a \Omega_M=0.28, \Omega_\Lambda=0.72, or thereabouts, universe is degenerate and also concordant with the freely coasting model.

Note that the SCC model is closed whereas the freely coasting is open, it is the Milne empty hyperbolic model.
There will be a difference between the two at large R(t).

Thank you for those other links I shall study them.

Garth