Redshift z

[coldcreation]

But GR is rather specific in that more energy density means more spherical. The most hyperbolic would be the models with zero mass.

 

~modest

 

Alright, lets start with a question.

 

 

Which of the following spacetime manifolds would appear to be consistent with observations, as viewed from our reference frame, and taking into consideration, redshift z, surface brightness tests, angular size of distant objects, and light curves or rise times and redshifts of distant SNe Ia?

 

 

 

This diagram represents three different spacetime manifolds in reduced dimension. These are three different geometric models of the universe. The scale ranges from the observer to the horizon. The 'concentric' circles represent spherical shells around the observer. The central illustration (B) represents a Euclidean manifold.

 

 

Note: the observer is located at the origin (at the center of either 'sphere' A, B, or C). The outer edge of each illustration represents the visible horizon (the edge of the visible universe). So each circle surrounding the origin represents about one billion light years extending outwards about 10 billion light years (to the the outer edge of each illustration).

 

Note too, this has only to do with observations. It has nothing to do (yet) with the interpretation of those observations (i.e., disregard whether the universe is believed to be expanding or not).

 

 

Which geometric manifold is consistent with observations in the look-back time?

 

 

 

CC

[quantumtopology]

Hmmm... I'll go for diagram C. Hope I don't flunk this one. B)

But interpreting surface brightness tests, number count tests, SNe Ia light curves or angular size observations, I have to admit it's hard not to be biased by perssonal preconceptions, and I think that happens to everybody.

I'll wait for your answers

[modest]

Which of the following manifolds would appear to be consistent with observations, as viewed from our reference frame, and taking into consideration, redshift z, surface brightness tests, angular size of distant objects, and light curves or rise times and redshifts of distant SNe Ia?

 

I like the approach. and I think I can give a direct answer. But, I wonder if we could clarify a couple things first.

 

Focusing on just one line so that it's clear what I'm referring to,

The blue observer is looking at the red and green galaxies. It's easy to say that the green galaxies are twice as far as the red galaxies, but I think this needs some clarification.

 

It takes light some time to get from green to red to blue. Let's say, just for the sake of argument, that the universe is expanding—the distance between any two dots is increasing with time. When the green galaxy emitted light that blue currently observes the universe was younger and smaller:

Later, when red emitted light that blue currently observes, the universe was a bit bigger,

And later again, when blue makes the observation the universe has expanded to its current size,

 

And here is the problem, even though the universe is "currently" this size, it doesn't mean that it appears this size to blue. Blue doesn't see red and green where they currently are. Blue sees them where they were when the universe was smaller because the light took time to get to blue.

 

If (for the sake of argument) the universe is expanding and green is currently twice as far from blue as red is from blue then the distance green-to-red will appear smaller to blue than the distance red-to-blue (even though the distances are currently the same).

 

 

So, looking at your diagram,

 

 

It's not clear to me what the lines should mean. You say each circle is an additional distance of about a billion lightyears, but a proper distance of a billion lightyears is different from a light travel time distance of a billion lightyears.

 

If the lines represent the proper distance then two spaceships at the red galaxy traveling the same speed in opposite directions (one toward green and the other toward blue) would both reach their destinations in the same amount of time. This is the kind of distance cosmologists mean when talking about the shape of the universe and in this case the universe appears flat. Standard cosmology in proper cosmological distance would be option B.

 

If the lines represent the light travel time distance which is to say that light took the same amount of time to get from green to red as it did red to blue (where red to blue happened later than green to red) then I believe C would be the correct rendition.

 

With that I should probably stop before it appears I'm ridiculously obfuscating. ;) I swear I'm not meaning to B)

 

~modest

 

 

EDIT--->

 

Ok, just a little more obfuscating :phones:

 

This might show better what I mean. In a truly hyperbolic universe (I couldn't find a good spacetime diagram of a flat one) the blue dots are the current proper distance and the green dots are the apparent light travel time distance (or look-back time) between those same galaxies:

 

 

As explained on Cosmology Tutorial - Part 2

 

The different distance measures would correlate to these dots on A and C:

 

 

In this case A is a slice of constant proper time and C is a slice along the past light cone. If the spacetime diagram were of a flat universe then the blue dots would be evenly spaced and would fit on B. The green dots would still be on C.

 

Note too, this has only to do with observations. It has nothing to do (yet) with the interpretation of those observations (i.e., disregard whether the universe is believed to be expanding or not).

 

:cheer:

[quantumtopology]

Ahaa, Modest so you noticed too how difficult it is to answer cc question without trying to frame it in a preconceived interpretation like a expanding or a static model or a specific geometry. But even consciously tring not to I also found hard to identify observations with one of the diagrams, so I am anxious to look at cc's solution B)

[modest]

Ahaa, Modest so you noticed too how difficult it is to answer cc question without trying to frame it in a preconceived interpretation like a expanding or a static model or a specific geometry.

 

Not only difficult, I believe it is impossible.

 

If you arrange real-world data in a manner consistent with CC's diagrams, like SDSS does here:

 

 

The radial distance is redshift. The 7 different distance markers are redshift z. In order to convert the redshift into units of actual distance like lightyears or meters we need a model with which to convert it.

 

For example, assuming the model is L-CDM then the comoving distances on the above image are...

z = 0.02 = 84.1 Mpc (0.274 Gly)

z = 0.04 = 167.5 Mpc (0.546 Gly)

z = 0.06 = 250.2 Mpc (0.816 Gly)

z = 0.08 = 332.2 Mpc (1.084 Gly)

z = 0.10 = 413.5 Mpc (1.349 Gly)

z = 0.12 = 494.0 Mpc (1.611 Gly)

z = 0.14 = 573.8 Mpc (1.872 Gly)

If the model were different (eg Lambda or rho had a different value) then the values of distance that correspond to those redshifts would be different. The same is true for luminosity distance and angular size distance, indeed all the observational distance measures.

 

The trick, then, to figuring out which model is correct and hence which diagram is correct, is to compare two different measures of distance for many different objects which is what SN1a redshift to brightness tests do.

 

But, yes, the concentric circles in CC's diagrams presumably represent distances which are not directly observable in the sense that we can't go out there and physically measure them. We have to interpret redshift, brightness, and angular size as a distance and that can't be done without a model.

 

~modest

[quantumtopology]

Ok, so if we center ourselves on the observations from the Supernovae, cause basically we agree they are the most reliable here, and we take diagram A as a model in wich sufficiently large distances are seen as bigger than they "really" are, model B without distorsion, and model C where we perceive distances as smaller than they are (at least this is how I interpret the diagrams), we find that:

Supernovae explosions are dimmer than we expected in a flat distorsionless scenario as if light was dispersed in a bigger volume than redshift Z predicts therefore we perceive as smaller what in fact is bigger wich leads to diagram C.

But nobody currently sees it this way because as soon as you have the belief in expansion engraved in your brain you just have to see it as an acceleration of expansion instead of in a geometrical way, you are obliged to interpret the dimmering effect kinematically.

So as Modest says there is no way to use observations without some model, that innocent view would be pure math, not physics.

The point where Modest and I cordially disagree is that he is convinced that the expansionist model is the only one that observations allow, and I am not. But wouldn't it be boring if we agreed on everything :coffee_n_pc:

[modest]

Ok, so if we center ourselves on the observations from the Supernovae, cause basically we agree they are the most reliable here, and we take diagram A as a model in wich sufficiently large distances are seen as bigger than they "really" are, model B without distorsion, and model C where we perceive distances as smaller than they are (at least this is how I interpret the diagrams), we find that:

Supernovae explosions are dimmer than we expected in a flat distorsionless scenario as if light was dispersed in a bigger volume than redshift Z predicts therefore we perceive as smaller what in fact is bigger wich leads to diagram C.

But nobody currently sees it this way

 

Yes, they do. Everyone knows that negative spatial curvature increases luminosity distance (lowering the apparent magnitude from what it would otherwise be). Likewise, everyone knows that positive curvature decreases the luminosity distance.

 

This fact is built into the FLRW metric. It's not being neglected.

 

What you have neglected is that redshift if it is indeed caused by recession increases the luminosity distance dramatically from what it would be if there were no physical recession. The effect of spatial curvature on the brightness to redshift relation is very small compared to the effect of expansion on the brightness to redshift relation. You've neglected the latter and fault cosmologists for neglecting the former (when they have not, in fact, neglected it at all).

 

If you want to propose that redshift is caused by something other than expansion then we're no longer talking about data that is slightly more dim then one would otherwise expect. It would be dimmer by leaps and bounds. All of the dimming due to expansion would need to be explained by some other means.

 

To explain it by some other means would require rejecting general relativity. Cosmologists are not merely reluctant to do this, they simply don't have a functioning alternative. In other words, if it ain't broke, don't fix it—especially if you have nothing to fix it with.

 

~modest

[quantumtopology]

Yes, they do. Everyone knows that negative spatial curvature increases luminosity distance (lowering the apparent magnitude from what it would otherwise be). Likewise, everyone knows that positive curvature decreases the luminosity distance.

 

This fact is built into the FLRW metric. It's not being neglected.

 

Great, so much for the better , would you mind explaining exactly how it is built into the FLRW metric? I thought the L-CDM model assumes a flat space so it's a bit contradictory with what you state.

 

What you have neglected is that redshift if it is indeed caused by recession

 

I am not neglecting it , I am just tryin to follow the rules of the riddle proposed by cc, so I avoided the expansion prejudice

 

 

 

If you want to propose that redshift is caused by something other than expansion then we're no longer talking about data that is slightly more dim then one would otherwise expect. It would be dimmer by leaps and bounds. All of the dimming due to expansion would need to be explained by some other means.

 

Exactly, that is what this long thread has been trying to do all along, explain redshift z and the dimming by some other means, I beleieve it is its only purpose.(Since It,s not closed I won't judge its succes in it) You speak as if you didn't know it.

 

To explain it by some other means would require rejecting general relativity.

I don't agree, maybe it would only require some minor changes.

In other words, if it ain't broke, don't fix it

But it is broke:Dark energy, dark matter, cosmological constant disparity, age problem,fine tunning ....

 

especially if you have nothing to fix it with.

As I said , that I believe to be the purpose of this thread,(well not to fix it just to humbly throw alternative ideas towards that end.

I would just like to follow cc's proposal which looks interesting, come on cc give us some feedback.:coffee_n_pc:

[modest]

Great, so much for the better , would you mind explaining exactly how it is built into the FLRW metric? I thought the L-CDM model assumes a flat space so it's a bit contradictory with what you state.

 

Sure. ΛCDM [math]\neq[/math] FLRW

 

ΛCDM, the model, is flat. FLRW, the metric, could be flat, hyperbolic, or spherical. The effects of spatial curvature are built into Friedmann and Lemaître's metric as explained here:

 

In such a universe, the interval (space-time separation) between events ("points" in space-time) can be described by the Robertson-Walker metric. By fixing the distances between all points, the metric also defines the geometry of space-time, and, because there is a meaningful cosmic time, the geometry of space at a given time. In fact, there are only three possibilities for the local geometry of space, because the curvature of space must be the same at all points (homogeneity) and not pick out any particular direction (isotropy):

 

Positive Curvature

The sum of the three angles of a triangle is more than 180°, (although this is only noticable for triangles with sides comperable to the radius of curvature, R). This case is denoted by setting the curvature constant k to +1. A 3-D space with positive curvature has a structure analogous to the 2-D surface of a sphere: if you travel far enough in any direction, you come back to where you started. Thus space is finite and the universe is said to be closed.

Flat space

The conventional geometry of Euclid. k = 0. This can be considered as the limit of the other two cases for infinite radius of curvature. Because it is balanced between the other two, this is sometimes called a critical universe. For true Euclidean geometry, the topology is also open, meaning that space is infinite in all directions. It is also possible to have compact topologies (e.g. the 3-torus) in a flat space, which have finite volume (and so are closed).

Negative Curvature

The sum of angles of a triangle is < 180°, (again, noticable only for very large triangles). k = -1. This is the hardest case to imagine as it is not even possible to have a 2-D surface of constant negative curvature (a pseudosphere) in Euclidean 3-D space. 2-D surfaces can have local regions of negative curvature, e.g. saddles and trumpet cones. The simplest topological case is when the universe is infinite in all directions, and so said to be open. In fact it is "more infinite" than the Euclidean case, in the sense that at a given distance from us there is more space than we would expect from Euclidean geometry. As for flat space, there are compact topologies with negative curvature, which are closed.

Robertson-Walker Metric

 

Or here: FLRW

 

 

By "built in" I specifically mean that a person can look at the rendition of different FLRW universes on a Hubble brightness diagram:

 

-source

 

and see that things should be less bright at a given redshift with lower mass density. Lower mass density with no Lambda means more and more hyperbolic, so the more and more hyperbolic a FLRW universe is, the less bright things are. This fact is built into the metric.

 

I am not neglecting it , I am just tryin to follow the rules of the riddle proposed by cc, so I avoided the expansion prejudice

 

Fair enough.

 

Exactly, that is what this long thread has been trying to do all along, explain redshift z and the dimming by some other means, I beleieve it is its only purpose.(Since It,s not closed I won't judge its succes in it) You speak as if you didn't know it.

 

You were surprised (for lack of a better word) that Sn1a tests were not interpreted with spatial curvature. I was explaining what that would entail—essentially, rejecting all of relativistic cosmology.

 

I don't agree, maybe it would only require some minor changes.

 

Unfortunately, general relativity is extremely well tested, so changes (even minor ones) would represent a different theory.

 

I certainly wouldn't rule out the possibility that a new theory of gravity will explain cosmological observations better than general relativity. But, I must insist, with general relativity the current observations can only be explained in an expanding model. To reject expansion as an explanation for cosmic observations is to reject general relativity.

 

But it is broke:Dark energy, dark matter, cosmological constant disparity, age problem,fine tunning ....

 

I might agree that Lambda is fine tuning. I don't think dark matter is. It was predicted by the rotation curves of galaxies. But, ΛCDM does exactly explain observations. It does correctly model our observations of the universe as an exact solution of general relativity. If it is to be falsified then we would need some observations that disagree with the model. If it is to be replaced, then we need a model that makes predictions at least as well as ΛCDM.

 

I wouldn't rule out the possibility, but currently I know of no such static model. In other words, before you fault cosmologists for not replacing standard cosmology with a static model, it would be good to have a static model that works.

 

As I said , that I believe to be the purpose of this thread,(well not to fix it just to humbly throw alternative ideas towards that end.

 

Now, that I agree with. It is always worthwhile to explore alternatives

 

~modest

[quantumtopology]

ΛCDM [math]\neq[/math] FLRW

I am aware of that , my question in fact was about the specific form of the metric used in LCDM, sorry about confusing it in the wording I used when asking.

 

Lower mass density with no Lambda means more and more hyperbolic, so the more and more hyperbolic a FLRW universe is, the less bright things are. This fact is built into the metric

Right.

Again, how is this fact built in the flat LCDM model (not in the general FLRW metric)?

 

 

 

I must insist, with general relativity the current observations can only be explained in an expanding model. To reject expansion as an explanation for cosmic observations is to reject general relativity.

We can perfectly agree to disagree on this particular point.

 

Regards

[modest]

I am aware of that , my question in fact was about the specific form of the metric used in LCDM, sorry about confusing it in the wording I used when asking.

 

 

Right.

Again, how is this fact built in the flat LCDM model (not in the general FLRW metric)?

 

:coffee_n_pc:

 

ΛCDM is flat (or very nearly flat with some uncertainty). It is like option B of CC's diagrams. Options A and C (hyperbolic and spherical) would be different FLRW universes—specifically, ones with more or less energy density than the critical density.

 

Asking how negative curvature is built into a flat model doesn't make any sense to me. It's like asking how the effect of curvature is built into a flat piece of paper. I don't understand what the question means or why you are asking it.

 

The point is that FLRW does allow you to curve the paper. It tells you why it would be curved and what the effects of curvature would be. Observations tell us that it is not curved which is why ΛCDM is flat.

 

We can perfectly agree to disagree on this particular point.

 

I gave the proof from Tolman in the other thread that there are only three static solutions to the field equations. None of them agree with observation, hence: no static cosmic solution of GR agrees with observation. To reject expansion is to reject GR. This is scientific fact. Disagreeing with scientific fact for no apparent reason is rather unscientific.

 

~modest

[quantumtopology]

You said that nobody was neglecting the fact that the observations of SNIa dimming could imply hyperbolic space and when I ask you why the standard model doesn't acknowledge this fact you say the question is absurd within te model, qed.So you are showing that in fact they are neglecting it as I first suggested. Certainly I wanted you to realize that contradiction.

 

I can give you some observation to ponder about the LCDM model Massive Ancient Galaxy Stirs Mystery: Is the Universe Older than We Think?

 

Regards

[modest]

You said that nobody was neglecting the fact that the observations of SNIa dimming could imply hyperbolic space

 

I see. No, I certainly didn't mean that hyperbolic space could be implied. I would not agree that observations of supernova standard candles imply hyperbolic geometry. This:

Everyone knows that negative spatial curvature increases

luminosity distance

(lowering the apparent magnitude from what it would otherwise be). Likewise, everyone knows that positive curvature decreases the luminosity distance.

 

This fact is built into the FLRW metric. It's not being neglected.

means that it is well known that hyperbolic curvature has the effect of dimming objects at a given redshift. This does not mean that our universe is hyperbolic or that negative curvature is the correct interpretation of SN1a tests.

 

The best fit for the data is [math]\Omega_{\Lambda} = 0.726 \pm .015[/math], [math]\Omega_{M} = 0.279 \pm .015[/math] which is within [math]\Omega_{K} = 0.015[/math] of being flat. The supernova are the correct brightness at all redshift with those parameters. They are not the correct brightness at all redshift for parameters that give significant negative curvature. The SN1a tests do not imply negative curvature.

 

I think you confused 'yes, everyone knows there is such an effect in relativistic cosmology' with 'yes, that is what is happening in the universe'. The former is correct, the latter is not.

 

and when I ask you why the standard model doesn't acknowledge this fact you say the question is absurd within te model, qed.So you are showing that in fact they are neglecting it as I first suggested. Certainly I wanted you to realize that contradiction.

 

You are again not making too much sense to me, so let's look at the actual data and remove all confusion,

 

 

I've cropped the image. you can get the whole thing here page 31.

 

Higher on the graph means fainter. Further right on the graph is higher redshift. The bottom black line is a spherical universe. The middle black line is flat and the top black line is the most hyperbolic of all relativistic models. This indicates that things are dimmer with less positive curvature and dimmer still with negative curvature. While curvature is not the only thing that has such an effect, it clearly does have that effect.

 

The top black line, which is the most hyperbolic, is not the best fit for the data (not to mention, it is an empty universe) so...

 

Introducing the cosmological constant, we can now work with the dotted blue lines. They are all flat. The best fit is between [math]\Omega_{\Lambda} = 1[/math], [math]\Omega_{M} = 0[/math] and [math]\Omega_{\Lambda} = 0.5[/math], [math]\Omega_{M} = 0.5[/math]. Lambda-CDM lies between those curves.

 

Hopefully this makes sense.

 

I can give you some observation to ponder about the LCDM model Massive Ancient Galaxy Stirs Mystery: Is the Universe Older than We Think?

 

Yes, we have discussed that galaxy on Hypo before. I don't recall which thread.

 

~modest

[coldcreation]

Good evening gentlemen,

 

Sorry for the delay in posting, I've been away from a computer for a few days. Meanwhile, back to civilization.

 

 

There is something I would like to rectify slightly from the initial diagram presenting three differing geometries. These three manifolds should not be the same size. Illustration (A) should be slightly larger, and © should be slightly smaller than than the Euclidean manifold (:).

 

Note: The illustrations are still far from accurately represented. For example, the inner spherical shells on each diagram should be closer to the same size, i.e., the universe should look quasi-Euclidean close to the origin (the observer) and the deviation from linearity should manifest itself increasingly with distance. Alas, it does not appear this way in the illustrations.

 

 

So here is a modification with the approximate scale ratio.

 

 

 

 

I understand that the problem here is difficult if not impossible without a model or two. So lets look at the Lambda-CDM model first:

 

 

The deviation from linearity observed in the SNe Ia data, from about z=1.0, differs from the prediction of an empty universe, but it is very small. The point is that the deviation from the prediction of an empty universe has a curve in it. See, for Fig 13 of Hubble Space Telescope Observations of Nine High-Redshift ESSENCE Supernovae, reproduced below:

 

 

 

 

 

 

The curvature (non-linearity) shown above is the reason why most cosmologists prefer models that require both cold dark matter (DM) and dark energy (DE) [a cosmological constant, lambda] in which the expansion of the universe changes in a complicated manner.

 

 

Let's look at some of the pre-1998 predictions and post-1998 implications for cosmology, before discussing the two types of non-linear regimes (A and C) illustrated above:

 

 

Before 1998; three predictions, or perceived possibilities:

 

 

• The favored possibility described the universe in which omega is precisely equal to one (Ω = 1), the critical density. There is a one-to-one relation between the density of the cosmos and its spatial curvature, i.e., this model has a flat, Euclidean manifold (with zero curvature). The velocity of expansion tends to zero as its radius approaches infinity.
   
   
  
• Ω > 1: this model has a closed spherical geometry; it expands and collapses to infinite density in a finite time. There is enough gravitating mass to halt the expansion and reverse it, leading to a big crunch.
   
   
  
• The model with Ω < 1 has a hyperbolic geometry and expands for ever, tending to infinity with a finite velocity. The galaxies are undecelerated as there is not enough gravitating mass to stop expansion or to slow it down.
  

 

 

Post-1998 SNe Ia data implications:

 

 

• Distant supernovae and their host galaxies appear to be receding slower than permitted by Hubble’s Law (the proportionality between redshift and apparent magnitude). The observations are consistent with an accelerating expansion of the cosmos. Recall that if galaxies were receding with
  less velocity in the past (in the look-back time)
  , it means that instead of decelerating, as predicted, the universe appears to be picking up speed, accelerating outward for the past few billion years.
  
  
   
  
  
   
  
  
• The large shells of radiation and material emitted by distant SNe Ia appear to have
  a greater area than they would in a topologically flat space
  , making the
  source look very faint
  .
  
  
   
  
  
   
  
  
• The visible universe appears
  larger, deeper
  , younger,
  and emptier than previously suspected
  .
  
  
   
  
  
   
  
  
• Unexpected
  dimness
  of early supernovae gives
  the impression they are further away than their redshifts indicate
  , altering the predicted structure of the cosmos.
  
  
   
  
  
   
  
  
• These observations indicate that a general modification of the pre-1998 standard canonical hot big bang model is required: 96 percent of the matter and energy in the universe is missing, or dark.
  
  
   
  
  
   
  
  
• Light from very remote objects takes longer to reach Earth—as if time and space (and the light propagating through it) were continually and increasingly ‘stretched’ with larger distances.
  
  
   
  
  
   
  
  
• The universe could be as young as 12.5 billion years old—a figure at odds with the age of some of the objects in it.
  
  

 

 

 

What good now is a theory that predicts a flat Euclidean universe if observations of distant SNe Ia reveal nonlinearity, implying that the universe is accelerating, i.e., not flat?

 

Without going into great detail, flatness was desired (for a variety of reasons), and flatness could be achieved, and would be achieved, by tweaking parameters. In other words, depending on how the parameters (DM & DE) are adjusted, one can attain the desired geometry.

 

 

What is more interesting, in my opinion, is to look at the actual data in relation to predictions made before the resurrection of lambda and nonbaryonic dark matter. But it is certainly interesting too, the way in which the SNe Ia observations would alter the cosmological landscape even with DM and DE.

 

 

So let me ask a question based on the SNe Ia data.

 

 

Which diagram, A, B or C, best describes the geometric structure of the cosmos (in the look-back time), as viewed for the reference frame of an observer?

 

 

PS. The answer now should be more straight forward. :D

 

 

 

CC

 

 

Edit: I'll get back to your posts shortly. Both of you made some very interesting remarks that I would like to comment on.

[modest]

The deviation from linearity observed in the SNe Ia data, from about z=1.0, differs from the prediction of an empty universe, but it is very small.

 

I agree.

 

The point is that the deviation from the prediction of an empty universe has a curve in it. See, for Fig 13 of Hubble Space Telescope Observations of Nine High-Redshift ESSENCE Supernovae, reproduced below:

 

The curvature (non-linearity) shown above is the reason why most cosmologists prefer models that require both cold dark matter (DM) and dark energy (DE) [a cosmological constant, lambda] in which the expansion of the universe changes in a complicated manner.

 

Ok, but non-linearity is being misapplied here. As odd as it might seem, the straight line in that graph is the hyperbolic universe and the curved line is the flat one.

 

An empty universe is the most hyperbolic you can get in GR. To find the curvature add [math]\Omega_{\Lambda}[/math] and [math]\Omega_{M}[/math]. If you get 1 then it is flat. If you get between 0 and 1 then it is hyperbolic. If you get > 1 then it is spherical.

 

The straight line in your image is [math]\Omega_{\Lambda} = 0[/math] and [math]\Omega_{M} = 0[/math]. It is the most hyperbolic of all Friedmann universes. The curved line is [math]\Omega_{\Lambda} = .73[/math] and [math]\Omega_{M} = .27[/math] (at least, without looking at the paper, I suspect it is something very near that) which is flat.

 

So the data, the SNe-Ia data, indicates a spatially flat universe. And, this is confirmed by, for example, the angular size of the peak temp. fluctuations in the CMB.

 

I strongly believe that our universe is best represented by option B in your diagram.

 

~modest

[quantumtopology]

So , I'll switch from C to A i f we refer to actual structure of the geometry and not to our representation of it.

Modest, I think your discrepancy with cc arises from the fact that you interpret the data after the tweaking has been done, and therefore you are already biased towards a certain result.

Try looking at the graph as if you knew nothing about LCDM or DM and DE. I know it must be hard, but those are the rules of the game as I see it.

 

Regards

[coldcreation]

Ok, but non-linearity is being misapplied here. [...]

 

Hey that was going to be my next one-liner!

 

 

So the data, the SNe-Ia data, indicates a spatially flat universe. [...]

 

I strongly believe that our universe is best represented by option B in your diagram.

 

~modest

 

Ok, but linearity is being misapplied here. :)

 

 

Interesting, isn't it, that such a remarkable fine-tuning would exist in nature, between the tendency to gravitationally attract, expansion and a repulsion of the vacuum. And that the manifold within which that transpires is Euclidean, despite the universe expanding out of control. Convenient too I might add.

 

 

So recap, what we had pre-SNe Ia data was the favored Friedmann model, and a flat geometry, with a probable zero value for Einstein's cosmological term. Then came the SNe Ia data.

 

In order to bypass the problem associated with those observations, which clearly pointed to manifold A above (i.e., a non-linear framework), CDM and DE had to be adjusted. But even a small adjustment in the hypothetical DE, for example, became a huge quantity, some 74% of the total mass-energy density of the universe. While the hypothetical cold dark matter accounts for 23% of the mass-energy density of the observable universe, In the mean time, the remainder, ordinary baryonic matter only accounts for only 4.6%.

 

 

The point to make is that without DE and CDM, and considering expansion according to the pre-1998 critical Friedmann model, non-linearity was clearly manifest. In other words Hubble's constant was no longer constant, it was no longer a law. There was no longer a one-to-one relation between the velocity at which various galaxies were receding from the Earth proportional to their distance from the observer. The Hubble Diagram, in which the velocity (assumed approximately proportional to the redshift) of an object plotted with respect to its distance from the observer was no longer a straight line. The scale factor of the universe could no longer be reconciled with the pre-1998 preferred model. It was larger. The ultimate fate of the universe looked entirely different than predicted.

 

 

One look is worth ten thousand words.

(Proverb from a fortune cookie in a NJ restaurant, 2005)

 

 

At that point, there were to options: (1) to consider the expanding universe hyperbolic, with a zero value for the cosmological term and accelerating; or (2) consider the expanding universe flat with a non-zero, non-negative value for the cosmological constant, and accelerating. Basically, that would change our manifold from diagram A to B (the Euclidean spacetime).

 

But let's be clear: Lambda-CDM has no explicit physical theory for the origin or physical nature of dark energy or cold dark energy.

 

But aside from that, it must strike the reader as curious (to say the least) that despite a supposed Euclidean manifold, (a) distant supernovae and their host galaxies appear to be receding slower than permitted by Hubble’s Law, ( the observations are consistent with an accelerating expansion of the cosmos, © the large shells of radiation and material emitted by distant SNe Ia appear to have a greater area than they would in a topologically flat space, making the source look (d) very faint. And despite a Euclidean manifold the visible universe appears (e) larger, deeper, and emptier than previously suspected, giving the impression they are (f) further away than their redshifts indicate, altering the predicted structure of the cosmos, and finally, that light from very remote objects (g) takes longer to reach Earth—as if time and space (and the light propagating through it) were continually and increasingly 'stretched' with larger distances; time dilation in supernova brightness curves (recall, frequency is inversely related to time).

 

All of the above constitute physical evidence that the universe is non-Euclidean. This is strong evidence for hyperbolic geometry of space on the cosmic scale. And the deviation from linearity appears to be large.

 

Indeed, if the expansion rate of the universe has actually been increasing, this should be concurrent with an open, hyperbolically curved universe.


 

 

In the upcoming posts I would like to discuss what would be the consequences or implications of the SNe Ia data in relation to spatiotemporal curvature of the manifold that is stationary, as opposed to expanding at an accelerated rate.

 

 

Astrophysicists are always wrong, but never in doubt.

(R.P. Kirshner)

 

 

 

CC