[modest]

Originally Posted by coldcreation

Obviously, any theory that is in disaccord with observations would have to be abandoned ("killed") or modified. In this case, the modification would not be an addition of DE or CDM, it would simply be a modification of the degree of curvature (a change in the gradient of the manifold) to agree with what is observed. The observations themselves determine the metric structure of spacetime.

Interesting. You say curvature doesn't have to depend on density. In a Friedmann model there are all those particulars about having to agree with general relativity where geometry and scale factor are determined by density hence the need for dark matter and the cosmological constant.

Maybe we should set some ground rules before we get too deep into this. I kind of just assumed any solution would have to agree with GR. Not the case?

~modest

[coldcreation]

Originally Posted by modest

Interesting. You say curvature doesn't have to depend on density.

I would suspect that curvature does depend on density. However, it had been shown (notably by de Sitter) that spacetime could be curved even in an empty world model.

So you bring up a very good point. What is the geometry of a universe (a vacuum) devoid of all matter and energy? This state is unattainable, but nevertheless, the question is a good one. I would assume such a space would be perfectly Euclidean geometrically, or Minkowskian, where special relativity is operational. But that may not be the case.

In the real universe, where all the laws of physics are operational, the vacuum is filled with ground-state energy, ZPE and fluctuations thereof. So even if all material components were to be removed, the vacuum would be non-Euclidean, since ground energy, ZPE, gravitate.

So the question remains open for debate.

Originally Posted by modest

In a Friedmann model there are all those particulars about having to agree with general relativity where geometry and scale factor are determined by density hence the need for dark matter and the cosmological constant.

Agreeing with GR is not the problem for the Friedmann model (all cosmologies should agree with GR). The problem for the Friedmann model is agreeing with observations. That is why there is the need of CDM and DE).

Originally Posted by modest

Maybe we should set some ground rules before we get too deep into this. I kind of just assumed any solution would have to agree with GR. Not the case?
~modest

Sure. Broadly: Any solution would have to agree with GR (as you state above). I would think the laws of nature should remain intact and operational at all times. Any solution would have to agree with observations.

The list could go on forever.

If you have any more important ones to add please feel free do so, but I think we should just get right to the heart of the debate: Is the Lobachevskian hyperbolic spacetime interpretation for cosmological redshift z in agreement with what is observed in the universe?

Perhaps we will find the answer to that question (or at least a partial one) in the work linked above. To answer this question fully and unequivocally will require a rigorous analysis of the observational data in the context of Lobachevskian hyperbolic spacetime.

Perhaps, then, a comparison can be made relative to the concordance model (Lambda-CDM) to see which interpretation best fits the data. And, which one does so with the least amount of parameter tweaking.



CC

[modest]

Originally Posted by coldcreation

I would suspect that curvature does depend on density. However, it had been shown (notably by de Sitter) that spacetime could be curved even in an empty world model.

So you bring up a very good point. What is the geometry of a universe (a vacuum) devoid of all matter and energy?

An empty universe (vacuum solution) is the most hyperbolic according to GR. This is true of FLRW, de Sitter's solution, Einstein's original model, or any other GR based cosmology. As more mass is added to these models, the density goes up and the geometry is less hyperbolic, flat, then spherical. Like I was saying, according to GR - geometry depends on density.

Originally Posted by coldcreation

Any solution would have to agree with GR (as you state above)

Very good. I'll get back to you when I've gone over the links.

~modest

[Pluto]

G'day from the land of ozzzzzz

Its funny that you two were talking about curvature

I was reading this paper

[0801.0304] Cosmological Perturbation Theory to second order for curvature, density, and gravity waves on FRW background; and the WMAP results of inhomogeneity and clustering in the early universe

Cosmological Perturbation Theory to second order for curvature, density, and gravity waves on FRW background; and the WMAP results of inhomogeneity and clustering in the early universe

Authors: Ajay Patwardhan, Kartik Prabhu, M.S.R. Kumar
(Submitted on 1 Jan 2008)

Abstract: The second order perturbation calculations for gravity wave and Einstein equation for space time and matter are presented for the FRW metric cosmological model. While exact equations are found, suitable approximations are made to obtain definite results. In the gravity wave case the small wavelength case allows nearly locally flat background for obtaining a fit to the WMAP data. In the density and curvature case the FRW background is retained for the length scale of WMAP. Clustering and inhomogeneity are understood. The gravity wave ripples from Big Bang couple nonlinearly and redistribute the modes to higher values of 'l' giving consistency with the WMAP results. The order by order consistency of Einstein equations relate the second order perturbations in the curvature and density and the wrinkles in spacetime caused by the gravity wave modes reorganize these distributions. The radiation data of WMAP gives the picture of a FRW spacetime deformed and wrinkled consistent with matter distribution to one hundred thousandths parts variation.

Darn ,just got a visitor,,,,,,I'll be back

[modest]

Originally Posted by coldcreation

Here is the pdf version of a link above (where the equations are easier to read): Big Bang as a Fatal Mistake of Edwin Hubble. Cosmological Red-shift and Related Electromagnetic Phenomena in Static Lobachevskian (Hyperbolic) Universe.

And here is an earlier article (2003) by J. G. von Brzeski and V. von Brezeski, on the same topic: Topological Wavelength Shifts, Elecromagnetic Field in Lobachevskian Geometry

Originally Posted by modest

Very nice Sr. Frío. When I have time (very soon I think) I'm going to go after these links enthusiastically.

These links are really captivating, coldcreation. I gave them a quick read which has forced me to review some basics on hyperbolic geometry and spacetime metrics in GR cosmology. It's taken a while, but I don't want to respond with any kind of opinion until I fully understand how they're getting what they have and what the implications are. It still may take a while yet.

I just wanted to compliment you on the links because I've looked before for papers with this content, but have been unable to find any, and also to let you know I have not forgotten them or brushed them off.

~modest

[Pluto]

G'day from the land of ozzzzzzzz

Reading the link,,,,,20 pages,,,,,,, posted by coldcreation

http://th-www.if.uj.edu.pl/acta/vol39/pdf/v39p1501.pdf
EXPANSION OF THE UNIVERSE — MISTAKE OF
EDWIN HUBBLE? COSMOLOGICAL REDSHIFT AND
RELATED ELECTROMAGNETIC PHENOMENA IN
STATIC LOBACHEVSKIAN (HYPERBOLIC) UNIVERSE

7. Conclusions and remarks
On the basis of a three-dimensional real Lobachevskian geometry, we
presented a geometrical analysis from which cosmological red-shift and related
phenomena follow in natural way. The presented equations give correct
numerical values for their respective physical quantities. The new Eqs. (15)
and (16) which relate red-shift to aberration might be useful in astronomical
observations.
Our presentation of Lobachevsky–Hubble cosmological redshift (5), the
Lobachevskian–Doppler effect (7), and aberration was done in rigorous way
on a purely geometrical basis of Lobachevskian three-dimensional real geometry
with all entities clearly defined. At present, the widely adopted view
explains cosmological red-shift using the vague concept of physical space inflation.
For example, observations tell us that space within galaxies, which
are rather diffuse objects, do not expand. Thus, where is the “border line”
in space which divides expanding space from non expanding space?
Next, we are told that inflation itself is due to some rather mysterious
event, which was sarcastically named by Fred Hoyle (to ridicule the whole
concept), as the big bang.
Instead, we offer an alternative solution based on simple Lobachevskian
geometry. We believe that looking at experimental data and Eq. (5), a much
simpler solution (minimum complexity solution) is to admit that the
space between distant sources and our spectrographs is negatively curved,
i.e. it is a Lobachevskian three-dimensional space causing the recorded
shifts. In other words what we see through our telescopes is the fundamental
formula of Lobachevskian geometry: Eq. (3). Experiments confirm our
model.
From the analysis performed, the importance of the range of applicability
of some mathematical notions follows. For example, someone who
only saw a map of the Earth as in Fig. 2, and had no prior knowledge where
this map came from, and what mechanism was used in mapping process, will
in good faith believe that Greenland is as big as the USA. His or her conclusions
about geography made from the distorted image will be necessarily
false.
Similarly, making conclusions about the geography of the universe based
on the so called “relativistic” formulas in the form of RHS expression in
Eq. (7) (and Eq. (6) as well), is misleading since we did not know that we
were looking at distorted formulas of a precise Eq. (3) of non-Euclidean
geometry projected into Euclidean space–space in our vicinity! Conclusions
based on a distorted formula will inevitably lead to the inconsistencies
and/or paradoxes for projections from regions of high distances d ≃ 1 in
space or high distances  ≃ 1 in velocities space. Of course, as long as we
stay “close to equator”, (which means going local, i.e. d ≪ 1,  ≪ 1) distortion
will be negligible within the required range of precision. Nevertheless
we have to be aware that we are still dealing with the distorted images.
This rises the serious question of applicability of the Special Relativity in
the range d ≃ 1,  ≃ 1.
One may ask a legitimate question of how the experimentally detected
cosmic microwave background radiation (CMBR) is related to Lobachevbreak
skian geometry (Lobachevskian universe)?
The answer is that in Lobachevskian space, CMBR is identified with
the homogeneous space of horospheres which is dual [7,9] to Lobachevskian
space. In our work [3] we showed that a horosphere in Lobachevskian space,
as far as physics is concerned, is a surface of constant phase of an electromagnetic
horospherical wave. In other words, it is a horospherical wavefront.
Radiation represented by horospherical wavefronts homogeneously
fills the entire Lobachevskian universe. Therefore, assuming a hyperbolic
universe, we have to have CMBR with its properties of homogeneity and
isotropy! It follows “automatically” from Lobachevskian geometry.
Horospherical waves are solutions of the Laplace–Beltrami operator (wave
operator) in Lobachevskian space. Their properties are well known and well
understood. Thus, there is entirely no need to associate CMBR with the
big bang — an event which itself cannot be understood and deliberated in
scientific terms.
In Lobachevskian space filled only with radiation CMBR would be perfectly
isotropic. In the presence of matter however, which on local scales is
distributed rather randomly, a small anisotropy in the properties of CMBR
might be present due to local conditions. This was already recorded by
COBE. More about the space of horospheres can be found in [7, 9].
The author wishes to acknowledge Vadim von Brzeski for his invaluable
comments.

Most interesting.

[Pluto]

G'day from the land of ozzzzzz

To add to the last link,,,,,,,,,
This link is quite interesting
The Magnetospheric Eternally Collapsing Object (MECO) Model of Galactic Black Ho

The Magnetospheric Eternally Collapsing Object (MECO) Model of Galactic Black Hole Candidates and Active Galactic Nuclei

Authors:
Robertson, Stanley L.; Leiter, Darryl J.

Publication Date:
00/2006 Origin: ADS

Abstract
The spectral, timing, and jet formation properties of neutron stars in low mass x-ray binary systems are influenced by the presence of central magnetic moments. Similar features shown by the galactic black hole candidates (GBHC) strongly suggest that their compact cores might be intrinsically magnetic as well. We show that the existence of intrinsically magnetic GBHC is consistent with a new class of solutions of the Einstein field equations of General Relativity. These solutions are based on a strict adherence to the Strong Principle of Equivalence (SPOE) requirement that the world lines of physical matter must remain timelike in all regions of spacetime. The new solutions emerge when the structure and radiation transfer properties of the energy momentum tensor on the right hand side of the Einstein field equations are appropriately chosen to dynamically enforce this SPOE requirement of timelike world line completeness. In this context, we find that the Einstein field equations allow the existence of highly red shifted, Magnetospheric, Eternally Collapsing Objects (MECO). MECO necessarily possess intrinsic magnetic moments and they do not have trapped surfaces that lead to event horizons and curvature singularities. Their most striking features are equipartition magnetic fields, pair plasma atmospheres and extreme gravitational redshifts. Since MECO lifetimes are orders of magnitude greater than a Hubble time, they provide an elegant and unified framework for understanding a broad range of observations of GBHC and active galactic nuclei. We examine their spectral, timing and jet formation properties and discuss characteristics that might lead to their confirmation.

[modest]

Originally Posted by coldcreation

Here is the pdf version of a link above (where the equations are easier to read): Big Bang as a Fatal Mistake of Edwin Hubble. Cosmological Red-shift and Related Electromagnetic Phenomena in Static Lobachevskian (Hyperbolic) Universe.

Ok. I give up. The physics is beyond me. I wanted to make an airtight case against this paper - but I’ve found it impossible given my understanding.

I’ll throw out a few thoughts and be done with the chasing of my tail.

• This paper in no way agrees with GR. It doesn’t try to and on occasion attacks cosmology that is purportedly based on GR for trying.
  
• I am not convinced at all that it demonstrates hyperbolic curvature any differently than the Robertson Walker metric. Given the same radius of curvature between RW and this paper, what different answers are expected? I tried hard to figure that out, and could not. Apparently the only difference is that RW tries to handle evolution of scale and this paper simply states that it’s impossible to do so. Looking particularly at the bottom of page 1512 and top of 1513 of the link above it says clearly that given some redshift, it is impossible to assign any value of scale or curvature. So, what prediction is it making?
  
• This paper makes no predictions. There is no brightness to distance formula nor any other quantitative test. It also doesn’t present a complete metric. It is at every turn vague and ambiguous and ultimately frustrating.

I'll stop there and see if anything sticks

~modest

[Pluto]

G'day from the land of ozzzzzzzz

I came across this link, if I repeat links,,,,,,,sorry


Anomalous redshifts in the spectra of extragalactic objects.
Anomalous redshifts in the spectra of extragalactic objects.
Astronomy and Astrophysics, v.309, p.335-344 (A&A Homepage)

Abstract

In this paper we show that strong statistical evidence has been available for many years showing that QSO redshifts in at least some cases are not caused by the expansion of the Universe. In a complicated world the number of unexpected associations that can be subjected to statistical test is very large and somewhere among the entire ensemble of such associations a few may seem of significance, if taken separately, which are only chance effects, however, occasioned by the profusion of cases in the ensemble. False associations of this kind show up readily as new data become available, since the original chance effects are unlikely to be repeated in the new data. An example was an algebraic formula for the sunspot number which caused a considerable stir early in the present century, the formula agreeing with sunspot numbers over many years with seemingly uncanny precision, only for the agreement to disappear as soon as new sunspot numbers came along. This well-known statistical trap cannot be claimed against the proposition that QSOs of high redshifts are sometimes physically associated with nearby galaxies. This proposition has now been exposed to statistical test for almost thirty years, and it survives in new data just as well as in old data. Additionally, a number of cases have come along with the years where actual physical connections have been detected between QSOs and nearby galaxies. Six of these cases are discussed in detail in the present paper. It is consistent with standard physics for redshifts to arise from doppler motions and also in radiation emitted by matter in a gravitational field, as well as from the cosmological expansion of the Universe. These other possibilities have been examined repeatedly over the years but have never been found to give convincing explanations for the QSO-nearby galaxy associations described above. One is therefore left with the non-standard possibility that different samples of matter can have different mass scales. No theory of how the QSO mass scale could be different from the usual galaxy mass scale has hitherto been found acceptable, with the consequence that most astrophysicists and cosmologists have felt justified in ignoring the evidence for anomalous redshifts, the thought being that what is known to be impossible remains impossible no matter how strong the evidence for it may be. The main purpose of the present paper is to question this mode of thinking. We show how, consistent with the quasi steady-state cosmological theory developed recently in a number of papers, it is possible for samples of material of different ages to have different mass scales.

You would think that with so much conflict over redshift there would be some form of scientific research to resolve issues.


Intrinsic nature of readshift makes research quite difficult.

How do we overcome this?

[modest]

Originally Posted by Pluto

You would think that with so much conflict over redshift there would be some form of scientific research to resolve issues...

How do we overcome this?

We could measure the brightness and redshift of millions of QSOs and galaxies in the most ambitious astronomical survey ever undertaken. Maybe that would qualify as "some form of scientific research".

SkyServer: About the SDSS

~modest