The Relationship Between Distance and Brightness in Cosmology

[rasp]

This is my 1st post ever, apologies and thanks in advance to all who read or respond. How does the actual size of all space (in linear distance dimensions) relate to the observable universe's event horizon? For example, imagine measuring out from the Earth a sphere whose radius is the event horizon (equivalent to the distance light has traveled since the Big Bang?). I imagine we would reach a particle (or observor) on the surface of that sphere, which would itself be able draw a vector length in all directions that light has traveled from it since the big bang. In one of these directions their event horizon will be a linear addition to a radius of our event horizon and will end at a third particle, which can continue the logic of viewing an event horizon in all directions. This process continued would argue for an infinite set of spheres and spatial lengths. As infinity is usually a sure sign of error, can someone explain the correct reasoning to me without using "advanced" (post college alegbra) math? Thanks kindly.

 

[marcus]

How does the actual size of all space (in linear distance dimensions) relate to the observable universe's event horizon?...

I take by actual size in linear distance dimensions you mean in terms of distance now at this moment----if you could temporarily freeze expansion so as to provide an opportunity to carefully measure distances by radar or some other conventional yardstick.

The observable part of the universe is normally considered to be a ball with us as center and radius about 45 billion lightyears. That is, the most distant matter from which we are now receiving light is today (partly because of expansion) slightly over 45 billion lightyears from us in actual distance.

That means if you could freeze expansion it would, starting today, take 45 billion years for a signal from us to reach that matter. We are seeing that matter (as it was over 13 billion years ago when it emitted the light) whenever we map the cosmic microwave background.

=======================
Since you are new to the board (*welcome* by the way!) maybe I should say that astronomers call the actual distance to an object at some given time (freezing expansion at that moment) its proper distance.

There is no simple relation between proper distance and light "travel time", because the rate of expansion has changed a lot in the past.

The jargon term astronomers use for this 45 billion lightyear distance is the "particle horizon". If shortly after the start of expansion our matter had sent out a particle at the speed of light then that particle would now be 45 billion lightyears from us (because of the combined effects of both expansion and the particle's own speed.)

The particle horizon is normally what is called the radius of the observable universe.
That is probably more than enough jargon
So let's get to your main question.
======================

The standard model cosmology that astronomers use comes in two flavors---infinite space and finite space.

The simplest finite space case is where there is a very slight positive curvature so that space closes on itself like the 3D analog of the 2D surface of a balloon.
The most recent authoritative complete set of cosmo data I know was published January 2009 and is called the WMAP5 data (the 5th year report from a certain NASA mission that measured cosmo parameters the most accurately so far.)
Essentially what they said is that (of course it could be the infinite space case but) in the simple finite case the radius of curvature would be at least 100 billion lightyears, so that the circumference would be at least 2 pi times that---in other words in round numbers at least 600.

That means if you could freeze expansion at this moment, and would set out at the speed of light, like a lightbeam pointed in some direction, it would take you at least 600 billion years to make the full circuit and get back home. But probably more.
We don't have a better estimate, but that gives something to compare with the figure of 45 billion lightyears for the particle horizon.

 

[sylas]

This is my 1st post ever, apologies and thanks in advance to all who read or respond. How does the actual size of all space (in linear distance dimensions) relate to the observable universe's event horizon? For example, imagine measuring out from the Earth a sphere whose radius is the event horizon (equivalent to the distance light has traveled since the Big Bang?). I imagine we would reach a particle (or observor) on the surface of that sphere, which would itself be able draw a vector length in all directions that light has traveled from it since the big bang. In one of these directions their event horizon will be a linear addition to a radius of our event horizon and will end at a third particle, which can continue the logic of viewing an event horizon in all directions. This process continued would argue for an infinite set of spheres and spatial lengths. As infinity is usually a sure sign of error, can someone explain the correct reasoning to me without using "advanced" (post college alegbra) math? Thanks kindly.

Basically, because the speed of light is finite, you cannot separate the idea of looking a long way without also looking back in time; and because the universe as we know it has a finite age, there's a hard limit to how far you can see.

(As a minor terminology quibble, the term "event horizon" usually means something rather different. It's usually the boundary between us and particles we can never see no matter how long we wait into the future; rather than how far we can see right now. Only certain kinds of expansion, involving "acceleration", actually have an event horizon in this sense.)

Cheers -- sylas

 

[marcus]

Rasp,

If you want some hands-on experience with the standard cosmo model, which doesn't require more than high school algebra (not even that really), try playing around with Ned Wright's cosmo calculator.

He teaches the cosmology course at UCLA and is one of the leaders in the field, plus he has a great introductory website for the general public!

To get the calculator just google "wright calculator".

Try plugging in some large redshifts (the symbol for redshift is "z")
and see what distances you get.
If you type in some large redshift like 1000 or 10000 into the z box and press the button called "general" it should give you the actual distance to matter which we are seeing now with that redshift (as it was a long time ago, of course).
You will get outputs like around 45 billion lightyears, as you might expect. Good thing to check that kind of thing hands on.

 

[rasp]

Thank you both for your input. Sylas, let me restate what i believe I learned, and please correct me if I'm wrong. 1) The observable universe can be considered as a sphere with Earth as its center having a radius of 13 billion light years (p.s. I thought it was closer to 14.5 billion) and that due to inflation there are some objects that are further away such that their light emitted 13 billion years ago has not yet reached us. 2) In a positively curved, closed finite model, the entire universe curves back upon itself such that it has a circumference of 600 billion light years. 3) The particle horizon is the proper distance that would be found if we could measure the distance "now" to those objects which we see emitting light 13 billion years ago and which are at the edge of our observable universe.
If that is the case, there are several questions I might ask, but the first that comes to mind is, "What is the the limit to our observable universe?" Is it the limits of our technology or something more fundamental like the current speed of light? Can I assume the sky goes completely dark in all directions exactly at the 13 billion light year range?

 

[marcus]

...please correct me if I'm wrong. 1) The observable universe can be considered as a sphere with Earth as its center having a radius of 13 billion light years (p.s. I thought it was closer to 14.5 billion) ...

... several questions I might ask, but the first that comes to mind is, "What is the the limit to our observable universe?" Is it the limits of our technology or something more fundamental like the current speed of light? Can I assume the sky goes completely dark in all directions exactly at the 13 billion light year range?

The age of the universe is estimated at 13-some billion years. For some years the prevailing estimate was 13.7, now some recent work has something like 13.4.

The presentday radius of the observable is estimated at 45 billion light years.
It has to be a lot more than 13.7 billion light years because the light could have traveled 13.7 billion light years on its own, without the help of expansion.
Expansion has an effect like savings-account interest. Every mile you put behind you gets increased by a little percentage bit each year, so you end up having a lot more miles behind you than expected. It works out in this case to a bit over 45 billion lightyears.

That is how far away, today, the most distant stuff we are seeing is.

The limit of the observable is a mathematical limit. We are very close to it with our presentday instruments. Within a few hundred thousand years of the theoretical limit to how far back in time. Future instruments will be able to probe deeper. The technical problem now is that back at the redshift of the microwave background the universe is a glowing hot fog that light can't get thru. We need instruments that see low energy neutrinos that were able to pass thru the fog and extend our vision that last little way. Mostly the limit is fundamental, but a small remaining part is technical.

Can I assume the sky goes completely dark in all directions exactly at the 13 billion light year range?

No. We can see way past the 13 billion lightyear range and the universe looks pretty much the same out there as here. Same kind of galaxies. Same kind of supernovas. Same kind of quasars, clusters, same average density if you allow for the effect of expansion with the passage of time etc etc.

And although we can't see past 45 billion lightyears, the assumption is that if you could go out there and look, that it would look very much the same now as it does here. Same kinds of stars, galaxies, clusters of galaxies etc etc. We have no reason to suppose it is different from here.

Astronomers have never found any evidence that an "edge" exists, so they normally don't assume that such a thing exists. It would be an unnecessary complication without there being any logical reason for it.

 

[Chronos]

If we had optical instruments of sufficient power, the EM universe would have an 'edge' somewhere near 13.3 billion lights years distant [z~1100].

 

[Rymer]

If we had optical instruments of sufficient power, the EM universe would have an 'edge' somewhere near 13.3 billion lights years distant [z~1100].

The surface of last scattering (or CMB) redshift is not really related to distance in the same way as a normal cosmological redshift. In order to talking in terms of distance, there needs to be a specific 'location' separation. For CMB the redshift (as a value of 1100) is time related. (with several assumptions -- ideal reversible gas model -- the distance related redshift would be about the square root of this value -- as a sort of 'average value'. This isn't very good as a number either in some ways -- more of a 'size' than a 'distance')

 

[Chalnoth]

The surface of last scattering (or CMB) redshift is not really related to distance in the same way as a normal cosmological redshift.

Huh? It most certainly is. It's exactly the same. Just further away than galaxies and whatnot.

 

[Rymer]

Actually, the confusion here seems to stem from assuming 'distance' and 'size' are the same. In general, they are not. One example using the initial question is that its only an assumption that you can infinitely string together these radial separations. What you are calculating is an infinite 'distance' -- which could exist in a finite sized space.

 

[Rymer]

Huh? It most certainly is. It's exactly the same. Just further away than galaxies and whatnot.

Definitely NOT. One place the surface of last scattering occurred is RIGHT HERE. It includes ALL the universe. Its displacement is in time.

 

[Chalnoth]

Definitely NOT. One place the surface of last scattering occurred is RIGHT HERE. It includes ALL the universe. Its displacement is is time.

That doesn't make the redshift interpretation any different. The surface of last scattering was right here about 13.7 billion years ago, this is true. But the part of the surface which we see today in CMB experiments was some 45 million light years away or so from this location when it was emitted.

 

[Rymer]

That doesn't make the redshift interpretation any different. The surface of last scattering was right here about 13.7 billion years ago, this is true. But the part of the surface which we see today in CMB experiments was some 45 million light years away or so from this location when it was emitted.

Yes, and so were many other places. The location must be specific to 'measure' a distance.
The 1100 number is a Wien Displacement of a blackbody 'peak'. That is not distance related. It is also not a recession velocity effect. It is related to energy (density) -- an adiabatic expansion. The 'size' of the universe would increase with about the square root of this value (depending on a +- 1 in determining z).

 

[Chalnoth]

Yes, and so were many other places. The location must be specific to 'measure' a distance.

Every place that was that far away is found within what we see as the CMB. So, pick a spot. Anywhere is fine, it's all the same distance in every direction.

The 1100 number is a Wien Displacement of a blackbody 'peak'.

True. This is a difference in how the redshift is measured compared with galaxies, because it is much more accurate to measure the redshifts of galaxies via their spectral lines (galaxies aren't very good black bodies). But it isn't a difference in the physics of how the redshift is produced.

 

[Rymer]

Every place that was that far away is found within what we see as the CMB. So, pick a spot. Anywhere is fine, it's all the same distance in every direction.


True. This is a difference in how the redshift is measured compared with galaxies, because it is much more accurate to measure the redshifts of galaxies via their spectral lines (galaxies aren't very good black bodies). But it isn't a difference in the physics of how the redshift is produced.

Pick a spot isn't allowed. Need to be much more specific than that.

The difference (if any) isn't in how the radiation is produced -- the issue is WHERE. For CMB it was 'produced' everywhere at that 'time'. This is NO distance reference. All it reflects is the 'cooling' since that 'time'. The 'cooling' is related to a size increase -- which is related the square root of the temperature -- if assumed to be an reversible ideal gas -- or that there is no energy loss in the universe (adiabatic). Specifically this redshift is NOT related directly to a recession velocity -- others are.

 

[Chalnoth]

Pick a spot isn't allowed. Need to be much more specific than that.

Why? It doesn't make a difference. Every single place that emitted the light we now see as the CMB came from a shell of matter that was, at that time, about 45 million light years away.

The difference (if any) isn't in how the radiation is produced -- the issue is WHERE. For CMB it was 'produced' everywhere at that 'time'.

Yes, but we don't see most of that. Most of that light is, today, very far away from us now, either because it was traveling in some other direction, or because it already passed us, or because it hasn't reached us yet. It is only that little bit of light that was emitted 45 million light years away and happened to be traveling in this direction that we see today.

All it reflects is the 'cooling' since that 'time'.

Well, it reflects that too. But we're also seeing the glow of actual matter that has been redshifted, in precisely the way that light from galaxies is redshifted.

The 'cooling' is related to a size increase -- which is related the square root of the temperature

Minor nitpick, but the temperature of photons scales linearly with the expansion. There is no square root involved. That is:

$$T \propto \frac{1}{a}$$

Specifically this redshift is NOT related directly to a recession velocity -- others are.

Actually, the redshift of other matter isn't directly related to recession velocity. What's important is the history of the expansion from the time the photons were emitted to today, not how fast the object was moving either now or when the light was emitted.

 

[Rymer]

Why? It doesn't make a difference. Every single place that emitted the light we now see as the CMB came from a shell of matter that was, at that time, about 45 million light years away.Yes, but we don't see most of that. Most of that light is, today, very far away from us now, either because it was traveling in some other direction, or because it already passed us, or because it hasn't reached us yet. It is only that little bit of light that was emitted 45 million light years away and happened to be traveling in this direction that we see today.Well, it reflects that too. But we're also seeing the glow of actual matter that has been redshifted, in precisely the way that light from galaxies is redshifted.Minor nitpick, but the temperature of photons scales linearly with the expansion. There is no square root involved. That is:

$$T \propto \frac{1}{a}$$Actually, the redshift of other matter isn't directly related to recession velocity. What's important is the history of the expansion from the time the photons were emitted to today, not how fast the object was moving either now or when the light was emitted.

Spot matters greatly. Must be related to a specific spot in co-moving space. CMB is ALL of co-moving space.

All we ever see is the 'little bit of light' that is headed our way -- not specific enough.
(That is all we ever see.)

Not exactly the same way -- normally we do NOT measure redshift from the blackbody radiation peak -- but from emission lines from excited atoms. Much different in source and in precision.

Yes, temperature is linear with Wien Displacement -- but an adiabatic process has constant total energy -- its temperature cools as the square of its increased size -- same as a radiation dropoff -- and as a reversible ideal gas. But size is not necessarily distance.
In this case it definitely isn't related to the apparent recession velocity of co-moving space.

That means the Hubble Law relation DOES NOT apply to CMB redshift since Hubble Law is only really true in co-moving space.

 

[Rymer]

Note: while redshift can be caused by several processes, the one that we call 'cosmological' is the one that obeys Hubble's Law. Hubble's Law is only truly valid in co-moving space -- in fact that could even in many cases be used as a definition of co-moving space.

Hubble's Law relates a recession velocity to distance.

 

[Chalnoth]

Spot matters greatly. Must be related to a specific spot in co-moving space. CMB is ALL of co-moving space.

Not the CMB that we observe. The CMB that we observe is only a small portion of the background radiation: that portion emitted by matter that was, when it was emitted, around 45 million light years away.

Not exactly the same way -- normally we do NOT measure redshift from the blackbody radiation peak -- but from emission lines from excited atoms. Much different in source and in precision.

That's not what I was saying, though. What I said was that the physics that generates the redshift is the same. Yes, it's measured differently, because we're talking about different physical systems. The CMB, for instance, comes from a physical system that produced a near perfect black-body spectrum at a very specific temperature. This makes measuring its redshift from its temperature an excellent way to measure it. Most other objects in the universe are very poor black bodies, and even if they are reasonably good ones, we don't necessarily know their intrinsic temperature. So looking for absorption/emission lines in their spectra is a much better way to go.

But this should be contrasted with the physics which produces the redshift in the CMB versus galaxies: it's exactly the same. Exactly. There is no difference in what causes the light of a galaxy to be redshifted and what causes the light of the CMB to be redshifted. And when we look at the CMB, we are actually looking at a specific shell of matter that emitted that light (what we are seeing is what made up the universe at that time: a nearly-uniform bath of cooling plasma, and we see a particular shell of that plasma determined by how long ago it cooled to the point that the photons could flow freely).

Yes, temperature is linear with Wien Displacement -- but an adiabatic process has constant total energy -- its temperature cools as the square of its increased size -- same as a radiation dropoff -- and as a reversible ideal gas. But size is not necessarily distance.

I believe you're talking about a non-relativistic gas here. Photons are quite relativistic.

In this case it definitely isn't related to the apparent recession velocity of co-moving space.

In no case is the cosmological redshift simply related to recession velocity. Sure, for very short distances, before the curvature of space-time becomes terribly important, the interpretation of redshift as recession velocity is reasonably good. But at larger distances it starts to make less and less sense. Most of the galaxies we observe are far beyond the point where approximating redshift as being due to recession velocity is even close to reasonable.

That means the Hubble Law relation DOES NOT apply to CMB redshift since Hubble Law is only really true in co-moving space.

Except it does.

 

[Rymer]

Not the CMB that we observe. The CMB that we observe is only a small portion of the background radiation: that portion emitted by matter that was, when it was emitted, around 45 million light years away.That's not what I was saying, though. What I said was that the physics that generates the redshift is the same. Yes, it's measured differently, because we're talking about different physical systems. The CMB, for instance, comes from a physical system that produced a near perfect black-body spectrum at a very specific temperature. This makes measuring its redshift from its temperature an excellent way to measure it. Most other objects in the universe are very poor black bodies, and even if they are reasonably good ones, we don't necessarily know their intrinsic temperature. So looking for absorption/emission lines in their spectra is a much better way to go.

But this should be contrasted with the physics which produces the redshift in the CMB versus galaxies: it's exactly the same. Exactly. There is no difference in what causes the light of a galaxy to be redshifted and what causes the light of the CMB to be redshifted. And when we look at the CMB, we are actually looking at a specific shell of matter that emitted that light (what we are seeing is what made up the universe at that time: a nearly-uniform bath of cooling plasma, and we see a particular shell of that plasma determined by how long ago it cooled to the point that the photons could flow freely).I believe you're talking about a non-relativistic gas here. Photons are quite relativistic.In no case is the cosmological redshift simply related to recession velocity. Sure, for very short distances, before the curvature of space-time becomes terribly important, the interpretation of redshift as recession velocity is reasonably good. But at larger distances it starts to make less and less sense. Most of the galaxies we observe are far beyond the point where approximating redshift as being due to recession velocity is even close to reasonable.Except it does.

Starting at the end: Except it does NOT. Hubble's Law is ONLY about recession velocity - distance relation -- and is only true exactly in co-moving space. CMB is not identifiable at a particularly place in co-moving space and therefore does not have a specific recession velocity. (Everything over some value isn't good enough.)

The simple inverse square relation can be shown as a basic relation for an adiabatic process -- one that has no energy loss, I don't see how 'relavistic' comes into it for this purpose.

Its definitely NOT just a simple temperature redshift one to relate to distance in the same manner as a recession velocity. The CMB redshift cannot be used in the same way as any other cosmological redshift. It may (or may not -- model dependent) have a similar resulting value -- but it is NOT a Hubble relation -- and therefore NOT a cosmological redshift.

 

[Chalnoth]

Starting at the end: Except it does NOT. Hubble's Law is ONLY about recession velocity - distance relation -- and is only true exactly in co-moving space. CMB is not identifiable at a particularly place in co-moving space and therefore does not have a specific recession velocity. (Everything over some value isn't good enough.)

Except the surface which we are currently viewing is identifiable as a specific surface in co-moving space. It isn't everywhere, even though you can see it in every direction. And it does have a very specific recession velocity, a recession velocity that can be computed from its redshift (if you know a few things like the density of the universe at that time, and the distance to this surface).

The simple inverse square relation can be shown as a basic relation for an adiabatic process -- one that has no energy loss, I don't see how 'relavistic' comes into it for this purpose.

Honestly, I'm not sure where you're getting this from. Could you show me the derivation you're talking about? Because it looks nothing like any relationship between temperature, expansion, and the ideal gas law I've ever seen.

Its definitely NOT just a simple temperature redshift one to relate to distance in the same manner as a recession velocity. The CMB redshift cannot be used in the same way as any other cosmological redshift. It may (or may not -- model dependent) have a similar resulting value -- but it is NOT a Hubble relation -- and therefore NOT a cosmological redshift.

You keep asserting this, but you also keep ignoring the other fact that I have pointed out: Cosmological redshifts for galaxies are also not simply related to their recession velocity. The total redshift of a photon that is emitted by a far-away galaxy is determined by how much the universe has expanded in the interim. Plus some usually minor perturbation based upon how fast the galaxy is moving with respect to the background. By large most of the redshift comes from the expansion of space.

And because the expansion of space has changed over time, it is just not possible to simply relate redshift to recession velocity. Now, it sort of works for very nearby galaxies, as I noted, because the expansion hasn't changed much in recent times. But get to reasonable redshifts, and interpreting redshift as only due to recession velocity no longer makes any sense.

 

[Rymer]

Except the surface which we are currently viewing is identifiable as a specific surface in co-moving space. It isn't everywhere, even though you can see it in every direction. And it does have a very specific recession velocity (though I'd have to go back and calculate exactly what that is...it isn't simply given by the redshift), a recession velocity that can be computed from its redshift (if you know a few things like the density of the universe at that time, and the distance to this surface).Honestly, I'm not sure where you're getting this from. Could you show me the derivation you're talking about? Because it looks nothing like any relationship between temperature, expansion, and the ideal gas law I've ever seen.You keep asserting this, but you also keep ignoring the other fact that I have pointed out: Cosmological redshifts for galaxies are also not simply related to their recession velocity. The total redshift of a photon that is emitted by a far-away galaxy is determined by how much the universe has expanded in the interim. Plus some usually minor perturbation based upon how fast the galaxy is moving with respect to the background. By large most of the redshift comes from the expansion of space.

And because the expansion of space has changed over time, it is just not possible to simply relate redshift to recession velocity. Now, it sort of works for very nearby galaxies, as I noted, because the expansion hasn't changed much in recent times. But get to reasonable redshifts, and interpreting redshift as only due to recession velocity no longer makes any sense.

You have your mind set one way and I totally disagree. I don't see any point in trying to convince you otherwise -- since you totally ignore what I'm telling you.

Our views of cosmology are just to divergent on too many points. You seem locked on the concept that the photons are being 'effected' in some way to produce the redshift.
I'm equally 'locked' in opposition to that belief. To me the (cosmological) photons themselves are un-effected by gravity -- redshift being due to a recession velocity due to an expanding universe. No gravity involved.

At this point in time the data is indeterminate (see thumbnails -- this also addresses you comparison questions for other postings/messages -- namely that the two results are so close that current data cannot choose between them).

However, our points of disagreement in this case are more fundamental than even these opposing theories. At least I thought I started out with the 'mainstream' view in this thread -- the expansion of the universe being an adiabatic process. (Adiabatic = constant energy (no loss) -- meaning energy density drops with the inverse 'size' squared -- and so does temperature -- basic thermodynamics. ) And Hubble's law valid in co-moving space. AND that distance is measured between two 'points' -- not randomly.Last post on this thread.

 

[Chalnoth]

You have your mind set one way and I totally disagree. I don't see any point in trying to convince you otherwise -- since you totally ignore what I'm telling you.

Our views of cosmology are just to divergent on too many points. You seem locked on the concept that the photons are being 'effected' in some way to produce the redshift.
I'm equally 'locked' in opposition to that belief. To me the (cosmological) photons themselves are un-effected by gravity -- redshift being due to a recession velocity due to an expanding universe. No gravity involved.

Yeah. Your view is wrong. Here is the SNLS year 1 data release:
http://xxx.lanl.gov/abs/astro-ph/0510447

In figure 5 they present their matter density/dark energy density plot. Your model would be on the origin of said plot. But the SNLS data alone rule that out at nearly the 4-sigma level. Things get fantastically worse when you add in baryon acoustic oscillation data.

At this point in time the data is indeterminate (see thumbnails -- this also addresses you comparison questions for other postings/messages -- namely that the two results are so close that current data cannot choose between them).

Sorry, but those plots show nothing of the sort. There is no analysis. There is no description of the two models. There is no examination of the errors. The paper I posted above does all this, and it completely rules out your model. And that's just one among a large number of supernova observations, with a mere 71 high-redshift supernovae, combined with 44 nearby supernovae.

 

[Rymer]

Yeah. Your view is wrong. Here is the SNLS year 1 data release:
http://xxx.lanl.gov/abs/astro-ph/0510447

In figure 5 they present their matter density/dark energy density plot. Your model would be on the origin of said plot. But the SNLS data alone rule that out at nearly the 4-sigma level. Things get fantastically worse when you add in baryon acoustic oscillation data.Sorry, but those plots show nothing of the sort. There is no analysis. There is no description of the two models. There is no examination of the errors. The paper I posted above does all this, and it completely rules out your model. And that's just one among a large number of supernova observations, with a mere 71 high-redshift supernovae, combined with 44 nearby supernovae.

The data is the same set as used by Ned Wright on his website. The Kowalski dataset is the best one we have and has 398 data points (arXiv:0804.4142).

The plotted model points on the first graph are from Ned Wrights online calculator -- using Ho=74.2 km/sec/Mpc (Adam Reiss' latest value May 2009 arXiv:0905.0695). It clearly shows that the two models give very close to the same answers -- and looking at the data scatter on our best dataset (Kowalski, et. al. 2008) it is obvious that our current data cannot even begin to choose between them.

From the data there is little to choose between them -- however, the orange line is a PURE theory line -- NO DATAFITTING -- and it nearly matches the Riess data determined relation (flat model with Omega=0.30 -- also the latest from a July 2009 paper -- arXiv:0907.4524).

The derivation of one of the key parameters for this relation is based on the gravity concept involving pair production. This is NOT a new all encompassing theory -- only viewed to be a possible starting point for further investigation -- time and data will tell.
(paper has been submitted to Independent Research Forum)

Note: the SNLS data matches perfectly to this model -- however due to its limited range of redshift and mostly low value -- it does little in choosing between theories -- of any recent kind. I have already provided you with the SNLS data comparisons.

 

[Chalnoth]

Sorry, Rymer, but merely eyeballing the data doesn't cut it. A little understanding of the law of large numbers would help here: when you have many datapoints, the mean of those datapoints is determined far more accurately than any single datapoint. So no, just because the line lies within the scatter does not mean that the data is consistent with the line. You have to be more careful than that.

 

[Rymer]

Sorry, Rymer, but merely eyeballing the data doesn't cut it. A little understanding of the law of large numbers would help here: when you have many datapoints, the mean of those datapoints is determined far more accurately than any single datapoint. So no, just because the line lies within the scatter does not mean that the data is consistent with the line. You have to be more careful than that.

Chalnoth -- I have been doing data fitting as part of my job for the last 35 years. So I know what I'm doing. The point is a visual presentation for those that don't. And in this case the visual is all that is needed -- if you are willing to look.

The data is so poor that quoting numbers is meaningless -- only thing that might show some very minor info is comparative fits with different models on the same data. BUT this is effectively impossible since I don't have the specifics needed to reproduce the so called Standard Models -- with dark energy, etc.

An additional problem exists here, namely the lack of a common data fitting approach due to the large difference in the nature of the theories. Further there are no coefficients in common. Note: this theory is at this point 'primitive' -- only have two parameters -- and only fitting one at a time -- and this only done for support of the theory values. Also any comparison to a different model with more parameters (and with some values provided from other sources) does not give a valid comparison.

A new plot of your out of date SNLS data is attached in a thumbnail. I had to guess at the Cepheid correction in an attempt to bring it up to the latest reported values.

 

[Chalnoth]

Chalnoth -- I have been doing data fitting as part of my job for the last 35 years. So I know what I'm doing. The point is a visual presentation for those that don't. And in this case the visual is all that is needed -- if you are willing to look.

Well, in this case the high-redshift data is in dramatic disagreement with your plot, even by eye. All the data points lie significantly below your line.

The data is so poor that quoting numbers is meaningless -- only thing that might show some very minor info is comparative fits with different models on the same data. BUT this is effectively impossible since I don't have the specifics needed to reproduce the so called Standard Models -- with dark energy, etc.

You should. It's not very difficult. All you need to know are the Friedmann equations and the relationship between H(z) and the distance.

And there is only one standard model of cosmology. That's why we call it the "standard model". It's the one with a cosmological constant.

An additional problem exists here, namely the lack of a common data fitting approach due to the large difference in the nature of the theories.

That's silly. All you need to know is how, in your theory, brightness is related to distance, and you can make a plot of distance versus redshift. In other words, precisely what you claim to have already done.

How is brightness related to distance in your model, anyway?

Also any comparison to a different model with more parameters (and with some values provided from other sources) does not give a valid comparison.

If those parameters are necessary to fit the data, it most certainly does. Simpler is not always better. The question is whether the preponderance of evidence supports adding the extra parameters, and in this case it unequivocally does. The existence of gravity is a pretty big clue here.