# Offshoot from 'Theoretically how far can one see in the universe'

1. Sep 8, 2009

### Rymer

Only comment on this is that most of this is correct WITHIN the current model used for the cosmological redshift. The model itself is NOT fully proved and the details -- such as the actual values of distances quoted -- are subject to change and revision of the model -- as is true for all scientific models.

Some statements -- like changes in the expansion rate and implied relative velocities greater than the speed of light are part of the unproved portion of the current model.

For all the talk about 'precision cosmology' we are still very far away from being able to claim that. (This claim seems to be more related to promoting money from various sources than to any real scientific accuracy.)

2. Sep 9, 2009

### Chalnoth

Re: Theoritically how far can one see in the universe

While in principle this is true, our limits on how much those distances can change are now quite small. The probability of a qualitative difference is essentially nil.

You keep saying this, but the evidence is strongly against you.

3. Sep 9, 2009

### Rymer

Re: Theoritically how far can one see in the universe

Not true -- or more accurately only within your model.

It's the same evidence for all models at this point -- the support for both is nearly identical.
So I guess this means the evidence is against your model too.

Chalnoth, you have a closed mind -- and remind me of the same kind of people that hounded Boltzmann to death a hundred years ago.

At this time there are only a few hundred data points that provide much in the determination of the cosmological redshift relation and their accuracy is very poor. The error needs to be decreased by at least an order of magnitude in order to be able to differentiate between the models.

The Standard Model at the moment is only a 'winner of a popularity contest' -- and is NOT scientifically proved or even supported as the best fit to the data. Further, it cannot even DERIVE much from theoretical point of view. I have never seen a derivation of the Hubble constant or for Omega matter --- both should be possible if the model is accurate.

Last edited: Sep 9, 2009
4. Sep 9, 2009

### Chalnoth

Re: Theoritically how far can one see in the universe

Except, as I've already pointed out, you are completely ignoring the majority of the evidence we have available to us. You have focused only upon the supernova evidence, and have ignored the copious amounts of other evidence, including that from the CMB, from baryon acoustic oscillations, from weak lensing, from cluster counts, etc.

When you consider the evidence as a whole, your video that there is no gravity at large scales is obviously false.

I'm not the one that's ignoring the evidence. Having an open mind is the willingness to change one's mind in response to evidence. You haven't even provided the minimum tests I asked for earlier (a chi square analysis, just on supernova data), while I have provided quite a bit of evidence.

That is a positively silly critique. Accuracy is not determined by theoretical motivation. Accuracy is determined by the evidence.

You might as well argue that clearly, people two hundred years ago couldn't have known that the sky is blue because they didn't understand how light interacts with atoms in our atmosphere.

5. Sep 9, 2009

### Rymer

Re: Theoritically how far can one see in the universe

You love to argue don't you. For Cosmological Redshift the ONLY data of importance is the higher redshift data with otherwise determined distance. Yes, mostly supernovae -- but some gamma ray burst and even a few other possibles (Tully-Fisher, etc).

As far as I'm aware the CMB data is not effected by the difference in these models. I do question some of the popular statements that have been made about CMB -- but that has nothing to do with the cosmological redshift relation.

YOU provide me with the dataset you want tested with chi^2 -- the method in detail you want used for the test -- a comparison/equivalent for Standard Model along with the detailed technique used to arrive at the values for that model.

The problem I have found is that the models by their nature require completely different fitting techniques. So what criteria are you saying to use to compare? How can you do a chi^2 with any meaning in such a case?

I'm willing to give it a shot if you can define a way to do it -- I have tried before and found no real difference. And that is the point. With current data it cannot be determined.

If there is a noticeable gravitational effect at large scale then the universe would unlikely to appear FLAT. The only explanation I've seen for a cosmological scaled gravity and a FLAT universe is 'coincidence'. Even the Dark Energy solution is a 'coincidence' solution. Do YOU have a different explanation (I don't like 'coincidence')?

Added note: my model does NOT require fitting to the data. There are derived values for all the parameters needed -- derived from theory. The fitting on this model is only used to confirm these values -- as much as they can be with the poor data.

Last edited: Sep 9, 2009
6. Sep 9, 2009

### Chalnoth

Re: Theoritically how far can one see in the universe

Except it's all interrelated. You can't just single out a single piece of experimental data, taken out of context of the whole body of evidence. That's called 'cherry picking'.

One of the most tightly-constrained parameters for the CMB is its angular diameter distance (measured from the average angular size of the fluctuations). And we also know its redshift to extremely high accuracy. So yes, it most definitely has quite a lot to do with the cosmological redshift relation.

Meh, don't worry so much about comparing against the standard model (yet). Just figure out the chi^2 for your "model" for, say, one set of supernova data (the SNLS data would be good here). And don't forget to show your work.

Clearly you don't know much of anything about what the chi^2 test means. As long as we have accurate error bars on the data points, it's possible to perform a simple chi^2 test on any theoretical model to see if it's at least a somewhat reasonable model. It's not a terribly robust check, but it's a good first-blush check.

The flatness problem is a separate issue that is solved by inflation.

P.S. Every model requires some degree of "fitting", as there are always at least some free parameters. Yours has the Hubble constant, for instance. Also (at the absolute least) the distance at which gravity "turns off".

Last edited: Sep 9, 2009
7. Sep 9, 2009

### Rymer

Re: Theoritically how far can one see in the universe

Actually, the Hubble constant is derived -- under some assumptions of course: 70.506

Inflation -- the genie -- pick the right value and it works. Non-sense.

YOU don't understand. My model does not require any fitting in the fully derived form.

And you are right -- I do NOT understand how to apply chi^2 to such a situation -- that is why I want to see how its applied to Standard Model first -- I want the issue to be the result and not the technique. So what is the Standard Model result?

8. Sep 9, 2009

### Chalnoth

Re: Theoritically how far can one see in the universe

Derived? How?

Inflation is not without its faults, but it nevertheless does solve the flatness problem, and its predictions match observation.

Wow, okay. Here is the chi^2 test:

$$\chi^2 = \sum_i \frac{(d_i - t_i)^2}{\sigma_i^2}$$
Here $$d_i$$ is the data value (in this case, it's typically the apparent magnitude of the supernova), $$t_i$$ is the theoretical value (which will be some function of the redshift, which is assumed to be perfectly-known), and $$\sigma_i$$ is the RMS uncertainty for that particular data point.

You then get a number. If your fit is a good one, then the number should be close to the number of data points. If the fit is very poor, then it will be many times the number of data points.

9. Sep 9, 2009

### Rymer

Re: Theoritically how far can one see in the universe

Assuming I calculated right -- with no comparison I have no idea.

OK: Derived value with NO CORRECTION: 3.785337 *398
Derived value with -0.0653 correction (implied by Riess May 2009): 3.436380 *398

As said before -- data is poor.
Fitting will take a little longer to do.

10. Sep 9, 2009

### Chalnoth

Re: Theoritically how far can one see in the universe

Right, which means it's a rather poor fit, between 2 and 3 sigma away from a proper fit.

This is one of the things about having lots of data points: even if, by eye, it looks like the fit line goes through the data points, the statistical power of having a large number of them may mean that the line is not explained at all by the data.

11. Sep 9, 2009

### Rymer

Re: Theoritically how far can one see in the universe

EXACTLY what I've been saying -- the data is too poor to make a determination.

When I check with a fit using Ned Wrights calculator and optimizing for a slope of one and offset of zero I get Chi^2 = 1326 == for my derived value above its 1368

So what does your basic Standard Model Flat fit result in?

With that data scatter the difference is meaningless.

Added: My comparable fitted result is about 1330 (corrected -- wrong fit)

Last edited: Sep 9, 2009
12. Sep 9, 2009

### Chalnoth

Re: Theoritically how far can one see in the universe

I'd have to calculate it. Got a link to the specific data that you used?

And by the way, no, the scatter is taken into account with the error bars on the data (provided the error bars are accurate, of course).

Last edited: Sep 9, 2009
13. Sep 9, 2009

### Rymer

Re: Theoritically how far can one see in the universe

OK -- rewriting for clarity:

398 datapoints from SCPunion

Used Ned Wrights Standard Model calculator iterating a slope of 1 and offset of 0 (to 6 decimal places) with a Reduced Major Axis fit (gives the lowest chi^2), result: 1326.34

Using my model iterating a slope of 1 and offset of 0 with a Reduced Major Axis fit gives 1329.75

The difference is statistically meaningless -- however there is one interesting difference: my model allows for the derivation of relation parameter values -- Standard Model does not (to my knowledge). The purely derived curve has a chi^2 = 1368

Yes. http://www.sgm-cosmology.org/SCPUnion_AllSNe.tex [Broken] From the Kowalski paper.

Hummm ... yes the data scatter is included in the algorithm -- HOWEVER the numerical difference between the two fits is meanlingless due to the large value.

Also, note Ned Wright's calculator includes some corrections that are not in my model at this point in time. However, my model does have some corrections for gravitation due to nearby supernovae (about 0.022c) using this correction gives a result of 1326.38

Too many apples and oranges.

Last edited by a moderator: May 4, 2017
14. Sep 9, 2009

### Chalnoth

Re: Theoritically how far can one see in the universe

Sorry, I went away from my computer for a bit. One more question: what is the redshift/distance relation you used in your model?

I'll get to producing the Chi^2 for a best-fit standard cosmology shortly.

15. Sep 9, 2009

### Rymer

Re: Theoritically how far can one see in the universe

My model starts with Doppler for Velocity, -- transforms it into an index in co-moving space using law of cosines and an expansion velocity, then using a 'distance reference' (and Hubble like relation) converts to co-moving distance, then (1+z) into luminosity distance, etc.
(Requires an iterative numerical solution.)

See: http://www.sqm-cosmology.org [Broken]

Last edited by a moderator: May 4, 2017
16. Sep 9, 2009

### Chalnoth

Re: Theoritically how far can one see in the universe

However, here's the Chi^2 I compute for the standard model, using the best-fit parameters in SCP Union paper, and the Riess et. al. (2009) value for the Hubble constant:

Chi^2 = 448.04

With N = 307 supernovae, this makes Chi^2/N = 1.46. That's a fairly decent fit. It's not quite Chi^2/N = 1, but then we don't expect it to be, as most real errors in data have longer tails than Gaussian. But in any case, this is a pretty good fit. There's no reason to suggest that it's wrong just from these data, anyway.

Contrast that with the Chi^2 you compute above: that's a horrible fit. Anyway, if you can provide a link that works, I can make some pretty pictures showing why you get such a better fit with the standard cosmology.

P.S. The exact parameters I use are:
$$\Omega_m = 0.287$$
$$\Omega_\Lambda = 0.713$$
$$H_0 = 74.2$$

Last edited by a moderator: May 4, 2017
17. Sep 9, 2009

### Chalnoth

Re: Theoritically how far can one see in the universe

Okay, I found your website, it's:

http://www.sgm-cosmology.org/ [Broken]

I don't see anywhere in there where you compute the luminosity distance from a given redshift. You seem to go from the redshift to a recession velocity, and from a luminosity distance to said recession velocity, but that's not a useful comparison as the recession velocity isn't a measured quantity. How do you go from a redshift to a luminosity distance in your model?

Last edited by a moderator: May 4, 2017
18. Sep 9, 2009

### Rymer

Re: Theoritically how far can one see in the universe

That is what requires the iteration.

/* 'd' is redshift velocity from Doppler */

double VI(long double d)
{
long double x,x0;
long double q=0.000000000000001;
long double D;

D=d/ev;
x0=0;
while(1)
{
x=1-cos(x0)+sqrt(D*D-sin(x0)*sin(x0));
while (x<0.0) x+=1.0;
x=(x+x0)/2;
if (Abs(x-x0)<=q)
break;
x0=x;
}

if (x0>=pi/2)
{
Err=1;
fprintf(stderr,"Warning: Data exceeds maximum possible for ev=%4.3lf at vi=%lf\n",ev,(double)(ev*x));
}

return((double)(x)*ev);
}

Returns a Velocity index that when scaled by (1+z)/ev and a distance constant gives the luminosity distance

Last edited by a moderator: May 4, 2017
19. Sep 9, 2009

### Chalnoth

Re: Theoritically how far can one see in the universe

What is your value for ev? And the distance constant?

20. Sep 9, 2009

### Rymer

Re: Theoritically how far can one see in the universe

FYI: My DERIVED result for the 'best fit' dataset for SCPUnion is:

Chi^2 = 395.346774 with 307 datapoints 1.287775 (unshifted)

Just for the fun of it I found the data shift value that would give the lowest Chi^2
Found -0.0853 (magnitude shift nearer) giving:
Chi^2 = 334.835791 with 307 datapoints 1.09067
(this was with the derived parameter values)