# Inconsistency in Concordance Model?

• JuanCasado
In summary, Juan, you are confusing the radius of the observable universe with the particle horizon. The Hubble radius is the distance at which light can travel within the Hubble time. The particle horizon is the distance at which light can travel within the time it would take for light to travel from the origin of the universe to the observer. The Hubble sphere is the sphere of center 0 (observer) and radius the distance that light can travel within the characteristic expansion time, that is the Hubble time : τ=1/H(t). So R=c τ. The wellknown definition of the Hubble radius is c/H(t)---essentially what you say. But this is not the radius of the observable. The mass within
JuanCasado
There is, in my view, a problem in the standard cosmological model (SCM), which, to the best of my knowledge, has not been discussed so far:

The radius of the observable universe grows with time at the speed of light. R refers to the Hubble radius or particle horizon. The Hubble sphere can be defined as the sphere of center 0 (observer) and radius the distance that light can travel within the characteristic expansion time, that is the Hubble time : τ=1/H(t).
So R=c τ.
A more detailed definition can be found at:
http://en.wikipedia.org/wiki/Particle_horizon
I am not referring with R to the radius of a physical entity, i. e. the scale distance, but to a theoretical construction, which coincides with the radius of the observable universe, since light coming from beyond has not had enough time to reach us nowadays.
According to SCM, in a flat universe the density equals the critical density, which is proportional to H squared (from the Friedman equation).
We have H ~ 1/ τ = c/c τ = c/R, so that ρ ~ 1/R2, meaning that the universe density decreases as R squared grows. Then the mass within the observable Universe M ~ R and should increase with time.

On the other hand, an accelerating Universe should have a decreasing mass within its observable portion since the radius of the observable Universe grows only linearly time, and some accelerated material should pass through this boundary.

How can we reconcile both statements?

JuanCasado said:
The radius of the observable universe grows with time at the speed of light.
This is not true, Juan.
There are some confusions in your post. I am sorry to have to point this out. The radius of the observable is about 46 billion LY at present and it is growing much faster than c. As a rough estimate it is growing at about 4.3 times c.

R refers to the Hubble radius or particle horizon.

It is impossible for R to refer to both these two since they are different by about a factor of 3. This is wellknown. You must read more. The particle horizon is about 46 Gly. The Hubble radius is only about 14 Gly.

The Hubble sphere can be defined as the sphere of center 0 (observer) and radius the distance that light can travel within the characteristic expansion time, that is the Hubble time : τ=1/H(t).
So R=c τ.

Now you have correctly defined R to be the Hubble radius! The wellknown definition of the Hubble radius is c/H(t)---essentially what you say. But this is not the radius of the observable.

which coincides with the radius of the observable universe,

No, Juan, it does not coincide, they are not the same.

Then the mass within the observable Universe ... should increase with time.

Yes! Indeed the mass inside the limits of the observable does increase with time! It is not proportional to the Hubble radius as you seem to think, but it definitely increases.

On the other hand, an accelerating Universe should have a decreasing mass within its observable portion since the radius of the observable Universe grows only linearly time, and some accelerated material should pass through this boundary.

Could you be thinking of something entirely different called the cosmological event horizon? This is not equal to the radius of the observable and it is not equal to the Hubble radius. It is about 16 Gly at present.
Also not sure what you mean by "accelerated material". Material is not moving in the usual sense. Distances increase at an increasing rate but the material is essentially stationary and is not being accelerated as normally understood.

Anyway literally what you say does not make sense because no material is passing out thru the particle horizon, the boundary of the observable universe.

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How do we define the radius of observable universe ? Is it limited by the telescope resolution or other factor like extreme red shift preventing from observation ?

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v2kkim said:
How do we define the radius of observable universe ? Is it limited by the telescope resolution or other factor like extreme red shift preventing from observation ?

Imagine that sometime around the first second of the bigbang some crud that would eventually become the solar system sends out a photon.
Suppose by great good fortune that photon manages not to hit anything and be scattered or absorbed.

How far from us, in today's distance, could that photon be now?

Something that starts at approximately zero distance, at the beginning of expansion---how far could it be away from us, extreme best case scenario.

With the present cosmo parameters (near flatness, 27% matter, 73% darkenergy, Hubblerate 71) it works out that the particle could be 46 billion lightyears from us today.

That is the particle horizon distance.

And it works both ways, there could ideally be some crud out there which did the reverse, which sent a photon in our direction, which in the extreme best case scenario would get thru and be received by us today. And that crud might have also formed a galaxy and planetary systems etc. But we don't observe them as they are today, we see the early universe version of them how they were 13.7 billion years ago.

====================
A good approximation to the particle horizon distance is simply the presentday distance of the material which radiated what we are now seeing as CMB. That is not quite so far, it is 45+ billion lightyears.
You can find a more exact estimate if you just google "wright calculator" and get Wright's Cosmo Calculator and put in redshift z = 1090, which is the CMB redshift and it will tell you that the current distance of the crud that radiated that ancient glow is now 45+ billion from here.

What limits actually visibility (besides the things you mentioned) is that before the year 380,000 (when CMB was released) space was not very transparent, it was full of partially ionized gas, which acts like fog. Like the hot gas on the surface of the sun doesn't let you look deeper in

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marcus said:
The Hubble radius is only about 14 Gly.

Now you have correctly defined R to be the Hubble radius! The wellknown definition of the Hubble radius is c/H(t)---essentially what you say.

Yes! Indeed the mass inside the limits of the observable does increase with time! It is not proportional to the Hubble radius as you seem to think, but it definitely increases.

Could you be thinking of something entirely different called the cosmological event horizon?

Also not sure what you mean by "accelerated material". Material is not moving in the usual sense. Distances increase at an increasing rate but the material is essentially stationary and is not being accelerated as normally understood.

Thank you for clarifying the confusion in terms. I was indeed referring to the Hubble radius as mathematically defined. I was not thinking on the cosmologic event horizon. I have the impresion that even if the Hubble radius and the radius of the observable universe do not coincide is merely a matter of reference frame. For instance, we can observe the CMB close to the limits of the observable universe placed today at ca. 45 billion light years , as you said, because of the expansion of the universe during the time elapsed since the emission of the photons we detect today, but these photons have traveled ca. 13 billion light years (by definition of light year). Whatever the measurement system we prefer, we will agree (I hope) we are referring to the same physical system (the last sacatering surface), which is relatively close to the boundary of the observable Universe. But this is an aside.
Anyway, I retain that you agree on the increase of the mass within the observable universe, which was my first important point.
By "accelerated material" I was referring to mass carried out by the accelerated expansion of the universe or, if you prefer, mass receding from the observer at an increasing velocity.
Am I (aproximately) right on that?

Hola Juan. What a coincidence I've just finished developing a new cosmo model which agrees with the DeLightS model in your 2003 and 2004 papers. In fact, I mention both papers right in the abstract! See

http://cifresmodel.blogspot.com/

There is a last item needed to finish it, and if you care to give a hand, the question is posted at

https://www.physicsforums.com/showthread.php?t=291625

The draft on the blog lacks some readability since greek letters Delta, Pi and lambda got changed to latin D P and l. I can mail you the doc file if you want.

To note, the global metric I arrived to is de Sitter. So this is in line with the ongoing work on de Sitter Relativity by Aldrovandi-Pereira and Licata-Chiatti.

Cheers,
Parvulus

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Hola Parvulus.
Thank you for your interest in my research.
Since this is not the topic of this thread, I'd prefer to deal with it elsewhere. Please send me your paper by mail.
Regards.

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JuanCasado said:
Since this is not the topic of this thread, I'd prefer to deal with it elsewhere.

You're right. However, I think I can mention one obvious inconsistency in the FRW metric that I overcome in my model.

In FRW matter has constant mass and constant equivalent energy m c^2 (c is constant), while photons have decreasing energy (h c / lambda) and decreasing equivalent mass (h / c lambda).

In my model both matter's mass and photons' mass equivalent are constant. And both matter's energy equivalent and photons' energy decrease at the same rate.

Which behaviour looks more consistent?

Well, the possible inconsistency discussed in this thread is not the same. I would be pleased to participate discussing your last question if you please post it in a new thread, in order to avoid a mix of different topics. Thank you for your enthousiasm.

marcus said:
...no material is passing out thru the particle horizon, the boundary of the observable universe.
However, see for instance the Nature article:
http://www.nature.com/news/2002/020813/full/news020812-2.html#B1
where you can read:
The problem stems from the observation in 1998 that the Universe's expansion seems to be speeding up. The most popular explanation for this is that there is a cosmological constant - a repulsive force that opposes gravity.
As things stand, other galaxies will eventually disappear as they zoom away from us faster than the speed of light. Then nothing that happens in those parts of the cosmos can affect us. Our world - and everywhere else - will be isolated behind a boundary called a de Sitter horizon.

To sum up, I quote some undisputed statements on this thread:

From Marcus:
Yes! Indeed the mass inside the limits of the observable does increase with time!
From Nature:
As things stand, other galaxies will eventually disappear as they zoom away from us faster than the speed of light. Then nothing that happens in those parts of the cosmos can affect us. Our world - and everywhere else - will be isolated behind a boundary called a de Sitter horizon.
At least one of those statements should be wrong, and both of them appear to be derived from the Concordance model!
That's why I said that this model could be inconsistent.

JuanCasado said:
At least one of those statements should be wrong,...

Why?

I don't see any inconsistency.

I am talking about the particle horizon, which is currently at a distance of 46 billion lightyears (and the boundary of all the matter that is observable).

The Nature article says it is talking about the deSitter horizon, which is quite different. It is currently at a distance of 16 billion lightyears. We see stuff that is way farther than that, almost three times farther.

You are confusing two basic concepts and seem to be saying that the model is inconsistent because you are confused about the definitions.

If you are having trouble grasping the basic definitions, then for heaven's sake ASK. Don't be shy about asking. Ask about the definitions and get someone to explain.
=================================

In case anyone else is reading this thread and is curious, the 16 billion lightyear horizon is also called the cosmological event horizon. It exists because of accelerated expansion. It is currently at a redshift of z=1.8, approximately.

Redshift 1.8 is a comparatively small redshift. There are lots of galaxies in the catalog with redshifts bigger than 1.8. Even some with redshifts bigger than 6. And the CMB matter is at redshift 1090. We see stuff that is way way beyond the cosmo event horizon.

But say you pick some nice looking galaxy with redshift slightly over 1.8. Just slightly beyond the horizon (whatever it is exactly.) The point is if you leave today traveling towards that galaxy at the speed of light you will never reach it. That is the definition essentially. Today you can not send a signal to someone in that galaxy, with the expectation that it will ever reach them. And someone living today in that galaxy cannot send us a radio message either, and expect it to get here.

But the galaxy is observable and will continue to be observable for billions of years. After all it is only at redshift 1.8! Our observable universe contains stuff that is much much farther away than that.

I hope some more knowledgeable person will correct me if I'm misstating anything here, and also if anybody is puzzled by the definitions of the various horizons, please ask!
Earlier in this thread I defined the particle horizon
https://www.physicsforums.com/showthread.php?p=2069511#post2069511
This is what astronomers consider to be the boundary of the observable universe.
It is the 46 billion lightyear distance mentioned earlier.

Have a look and make sure you can tell the difference

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Hola Parvulus,

Since the discussion about the inconsistency I pointed out seems to be closed, we can talk about the one you pointed out, since as far as I know you have not initiated any new thread on it.
As proponent of DeLightS model, I should agree with you, but I think your model and mine's has an important problem also, which I would like to discuss with you as soon as I receive your paper (I've sent a mail to your adress).
Please let me know If this procedure is OK for you.
Regards

## 1. What is the Concordance Model?

The Concordance Model is a statistical model used in science to measure the agreement between two or more observers or raters. It is commonly used in fields such as psychology, medicine, and education to assess the reliability of measurements or ratings.

## 2. What is Inconsistency in the Concordance Model?

Inconsistency in the Concordance Model refers to a lack of agreement between two or more observers or raters. It can occur due to differences in interpretation, subjective biases, or errors in measurement. Inconsistency can affect the reliability and validity of the data being collected.

## 3. How is Inconsistency measured in the Concordance Model?

Inconsistency in the Concordance Model is typically measured using a statistical measure called the inter-rater or inter-observer agreement, which calculates the level of agreement between two or more raters or observers. This can be expressed as a percentage, with higher percentages indicating more consistency.

## 4. What are the consequences of Inconsistency in the Concordance Model?

Inconsistency in the Concordance Model can lead to inaccurate or unreliable data, as well as reduced validity and generalizability of the results. It can also increase the time and resources needed to collect and analyze data, as well as potentially impacting the overall conclusions of a study.

## 5. How can Inconsistency be minimized in the Concordance Model?

Inconsistency in the Concordance Model can be minimized by ensuring clear and standardized measurement procedures, providing proper training and calibration for raters or observers, and using multiple raters or observers to increase reliability. It is also important to address and resolve any discrepancies or disagreements between raters or observers during the data collection process.

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