a-cosmology-group/acg#308

We’re obviously in the infancy stages of learning about the higher-than-high redshift (z > 7 according to the table in a comment below), but what sort of preliminary picture is this painting for galaxy distribution?

If z=25 is 43 Gly away, and z~4 is 21.3 Gly away by your calculator, that would mean that z=4 is about half way to z=25.

If you consider that distance to be 1 unit, then the number of galaxies from 4 < z < 25 should be $2^3 - 1$ times as many as from 0 < z < 4.

Of course current galaxy counts are not indicative of what’s really out there, or what we may know decades and centuries from now… but doesn’t that seem a little far fetched? We don’t see 7 times as many galaxies out there. We see a billionth of the galaxies.

It’s so early to be drawing any conclusions of course, but still. Doesn’t that seem a little… not right?

For what it’s worth, in the comoving volume, the expanding universe paints a similarly absurd picture.

By contrast, (as we’ve talked about before), in my non-expanding model, which is like a de Sitter universe but with angular diameter distances only, the redshift-distance law is:

$$d = \frac{z}{1+z} \frac{c}{H}$$

So as $z$ approaches infinity, $d$ approaches ~13.8 Gly (assuming H=70 km/s/Mpc).

Dividing a sphere with a radius of ~13.8 Gly (or any number actually) into 4 equal parts yields these z ranges:

• 0.0000 < z < 1.7024
• 1.7024 < z < 3.8473
• 3.8473 < z < 9.9362
• 9.9362 < z < infinity

In this model, we would expect the number of galaxies with z > 10 to be equal to the number of galaxies with z < 1.7.

Doesn’t that seem at least a tad more realistic?

@mikehelland >Dividing a sphere with a radius of ~13.8 Gly (or any number actually) into 4 equal parts…

I’m not sure what you mean by that. Are you dividing the radius by 4 or the volume? If you are dividing the radius then you aren’t getting four equal volumes If you are dividing a volume then how are you dividing it up???

I don’t understand how your model is distinct from the standard model yet yields the same results using the same terms and units. If you are assuming H=70 km/s/Mpc then z has to be in km/s and you are basically using an expanding universe framework. As I understand it, a de Sitter universe is also expanding (and massless) with a cosmological constant. The difference seems to be that you are treating 13.8 Gly as a distance (to a boundary?) while the BB people see it primarily as a time indicator (the age of the universe). At least that’s how I (mis)understand you at this point.

As far as the 8 fold increase in a galaxy count when the observational range doubles (assuming an average galactic density) that is straightforward geometry. Regarding that you say:

We don’t see 7 times as many galaxies out there. We see a billionth of the galaxies.

It’s so early to be drawing any conclusions of course, but still. Doesn’t that seem a little… not right?

Yes, given the limits of our observational technology and that we only make distant observations through fortuitous “windows” in the local cosmos, I think you’re right, no conclusion is justified. We are after all observing only a small portion of that outer shell (defined by the doubled radius). We should expect to see a galactic density approximately like a similar scale interior volume - except of course that at the limits our current technology we will only detect the brightest sources.

So, it seems to me that the straightforward geometry + average density calculation that a 7x larger volume (the outer shell) will contain 7x as many galaxies as the interior volume remains a reasonable expectation, one that current observations can neither confirm nor refute. The only real question is whether there is an average galactic density that is scale independent over a cosmologically meaningful range.

Even the galactic density of the local cosmos <100Mly is not as well established as you might think it would be. If anything like a hard count has been done I haven’t found it. It is claimed that the local cosmos is under-dense but is that a consequence of misinterpreting a to-be-expected higher number count at larger radial distances?

Are you dividing the radius by 4 or the volume?

Volume.

If you are dividing a volume then how are you dividing it up???

Calculate the volume of the whole sphere, and then decide how many pieces you want it divided into. Say 100. So divide the whole sphere by 100, call it V100.

Find the radius it takes to make a sphere with volume V100.

Then multiply V100 volume by 2, and find its radius.

Then multiply V100 by 3, and find its radius. Etc.

Demo:

https://mikehelland.github.io/hubbles-law/other/sdss.htm

Source code:

https://github.com/mikehelland/hubbles-law/blob/master/other/sdss.htm

Click “Divide the volume by” and move the slider around. The resulting z bins are shown below. You’ll have to scroll down to see them listed.

z is unitless, by the way. It’s not a velocity.

Yes, z is unitless but in the standard model it equates to a recessional velocity and you’re employing the standard model term H which is a recessional-velocity/distance term to arrive at a z related distance so how is that not a recessional velocity model?

I’m also trying to understand what your model says about the physics of the Cosmos and it seems to be saying that the Cosmos has a hard boundary condition at 13.8Gly, is that correct?

Well… in the standard model things aren’t moving away so much, as the distance between things is increasing.

So there isn’t recessional velocity per se, but there is a scale factor $a$, the ratio between a distance now and that distance at some point in the past. The same ratio describes the wavelength of light when it is observed to when it was emitted.

$$1+z = a^{-1} = \frac{\lambda_{obs}}{\lambda_{emit}}$$

In my model, an observer has access to a spherical region centered on them with a radius of c/H where z=infinity at the sphere’s surface. We aren’t causally connected to anything beyond that.

What I’m pointing out to you is that your model uses a recessional velocity term which comes from the standard model. I am intimately familiar with the SM bullshit about expanding spacetime which is just a math-based song and dance to cover up the fact that the original assumption of redshift=recessional velocity proved wrong early on and doesn’t make physical sense because the recessional velocities implied quickly started trending toward the speed of light. That was the main reason Hubble objected to the RV interpretation.

Essentially by using the RV based term H you are just attributing the energy loss indicated by the redshift to a recessional velocity or at least your math is. Maybe that’s not what you mean but that’s what the math means. If that is not what you mean then to what do you attribute the cause of the redshift and why isn’t it reflected in the math?

Redshift z is the ratio of observed wavelength to the emitted wavelength minus 1.

Hubble’s constant can be in units of km/s/Mpc, but its actual dimensions are inverse time, because the km and Mpc cancel each other out.

There’s nothing that says recessional velocity is necessary.

In fact, my first adventures in alternative cosmology were based on the realization that if the photon lost 70 km/s for every Mpc it traveled, it would reach its destination at the same time and with the same energy as if it stayed at a constant speed and the destination was moving away.

I took the 70 km/s/Mpc out of the recessional velocity, and used it to affect light speed. A version of tired light where it doesn’t just lose energy, it loses velocity too.

I’ve since moved away from that idea though. My current conjecture is that time is speeding up, and therefore time was slower in the past. Light doesn’t actually redshift on its way through the universe. It basically started it out like that.

In this case it’s more logical to think of H as in the units of inverse time, not a velocity per distance.

“…time is speeding up, and therefore time was slower in the past.”

All that does is substitute one reified relational concept, speeding-up time, for the more common variant, expanding space. There is absolutely no scientific evidence to support the existence of a causally-interacting space, time, and/or spacetime. You are also borrowing a universal (space)time frame from the standard model.

Your efforts to fashion an alternative cosmological model are praiseworthy, but using an ad hoc mechanism and axiomatic assumption of the standard model to support your own ideas does not bode well for achieving a model that is physically realistic or scientifically meaningful.

All that does is substitute one reified relational concept, speeding-up time, for the more common variant, expanding space.

It also accommodates the observed phenomenon of cosmological time dilation, whereas tired light cannot.

There is absolutely no scientific evidence to support the existence of a causally-interacting space, time, and/or spacetime. You are also borrowing a universal (space)time frame from the standard model.

You may be reading a bit too much into my reference to the de Sitter universe. To clarify:

In the standard model (LCDM) mass/gravity pull back on the expansion of space, and there was a big bang singularity in the past.

Neither of those are true for the de Sitter universe. It is an exponentially expanding universe, which means, going backwards in time is exponentially contracting. It keeps getting smaller, but it never makes it to zero. There is no age of the universe in that model.

The de Sitter model was proposed around 1918, before Hubble showed that Andromeda is a galaxy outside the Milky way (1924) and that galaxies have redshifts correlated to their distance from us (1929).

Technically, in the de Sitter universe, our spacetime is the 4-dimensional surface of a 5-dimensional hyperboloid.

I didn’t borrow any of that. It just so happens that its redshift to angular diameter distance equation is the same as the equation I came up with for redshift-distance in my simulations (originally of tired light, but now interpreted as the past being slower than the present).

While the de Sitter model isn’t favored by anyone, it is well known, basically because it’s much simpler than the standard model, and usually taught before LCDM.

So my model coincidentally mimics one small part of the well known de Sitter model. That’s it.

Your efforts to fashion an alternative cosmological model are praiseworthy, but using an ad hoc mechanism and axiomatic assumption of the standard model to support your own ideas does not bode well for achieving a model that is physically realistic or scientifically meaningful.

While I disagree with your assessment, the topic at hand was how many galaxies are out there at these super-high redshifts.

I was asking Louis about his model’s predictions for galaxy counts in certain redshift ranges.

E.g., How many galaxies will be between z=10 and z=20? How many with z>20?

My model make pretty clear predictions on that.

Ptolemy’s math made clear and correct predictions but the physics it described was completely wrong. Math is not physics. Math is not science. Math is a necessary and useful modeling tool for science, but that is all it is - a tool.

De Sitter, like FLRW assumed that the Cosmo is a simultaneously interconnected entity that you could slap a universal frame on and do some meaningful calculations using a mathematical framework, General Relativity, that does not include a universal frame. That was the equivalent of Ptolemy’s geocentric assumption - a basic misunderstanding about the nature of physical reality.

Your model, however you distinguish it from de Sitter or FLRW, shares that misconception. It also shares the modern conceit of a substantival spacetime. It is just another mathematical model that is structurally discordant with actual physics. Any predictive successes of the model will only be Ptolemaic in nature. Mathematical models that are built on empirically baseless but mathematically convenient conjectures might be useful - as Ptolemy’s model was. They just won’t have any physical meaning or long-term scientific value.

Mathematical models that are built on empirically baseless but mathematically convenient conjectures might be useful - as Ptolemy’s model was. They just won’t have any physical meaning or long-term scientific value.

The empirical basis is cosmic time dilation.

There is another thread, #160 for the Time Dilated Past Hypothesis. You can follow up there if you’d like.

This thread is about the highest observed redshift candidates, and what different models have to say about how much stuff is out there.

If this z=25 galaxy is correct, as Louis says, it’s 43 Gly away, while a z=4 galaxy is half that distance. That’s a vastly huge space out there with only a relatively few galaxies in it.

It seems like there should be trillions of more galaxies at high redshifts than what’s been observed so far.

But if there is a cosmic horizon ~14 Gly away, then it seems to make more sense. z=20 and z=200 and z=20,000 are actually really close together.

The empirical basis is cosmic time dilation.

The point is that there is no empirical basis for the concept of a cosmic time frame. All of our observations are made in the context of our local frame. That local frame extends out to the limits of our observational horizon, but that horizon does not define a meaningful universal frame.

There is no empirical evidence for a universal (cosmic) frame because such a frame cannot be observed only assumed, and that is because the speed of light has a finite maximum. The observed time dilation relative to distant objects is not evidence for a cosmic frame anymore than the redshift is.

The point is that there is no empirical basis for the concept of a cosmic time frame.

Then don’t assume one. And start another thread if you feel compelled to discuss this further.

Hi @mikehelland and @budrap00 . Wouldn’t a bit of mathematics clarify some? Here goes.

Determine distance $d_1$ such that the maximum distance $d_N = (c/H)$ is divided in $N$ equal volumes.

$$ N.\frac{4}{3}\pi d_1^3 = \frac{4}{3}\pi \left(\frac{c}{H}\right)^3 \quad \Longrightarrow \quad d_1 = N^{-1/3}. \frac{c}{H} $$

And in general:

$$ \frac{4}{3}\pi d_n^3 = n.\frac{4}{3}\pi d_1^3 \quad \Longrightarrow \quad d_n = n^{1/3}.d_1 = \left(\frac{n}{N}\right)^{1/3}\frac{c}{H} $$

From Mike’s redshift formula:

$$ d_n = \frac{z_n}{1+z_n}\frac{c}{H} \quad \Longrightarrow \quad z_n = \frac{d_n}{c/H-d_n} = \frac{(n/N)^{1/3}c/H}{c/H-(n/N)^{1/3}c/H} = \frac{1}{(N/n)^{1/3}-1} $$

whch is independent of any assumed size $(c/H)$ of cosmos. Let’s check for $N=4$ .

z_0 := 0;
z_1 := evalf(1/((4/1)^(1/3)-1));
z_2 := evalf(1/((4/2)^(1/3)-1));
z_3 := evalf(1/((4/3)^(1/3)-1));
z_4 := infinity;

The outcomes are - of course - in complete agreement with Mike’s findings. No need to repeat them here.

Then don’t assume one. And start another thread if you feel compelled to discuss this further.

It is you who appears to be positing a universal timeframe at least that’s what you seem to be attributing the redshift to. Maybe not but you don’t seem to be able to provide any causal mechanism beyond “speeding-up time” and whatever it is you mean by that. Absent any further elaboration attributing a physical effect to a relational concept like time is just metaphysical handwaving.

The axis on the left accounts for ‘number of observations’ while the bottom axis accounts for ‘redshift z’ Increasing the ‘Absolute magnitude threshold’ seems to eliminate closeby readings which makes sense. Clicking ‘divide by volume’ increases the resolution but doesn’t seem to change the shape of the graph much. I would have expected the reading per volume to tend toward a flat line, if sufficient readings exist. It seems samples per volume taper off just like samples per redshift?

If the readings are ‘per volume’ as per settings, then ultimately we should end up with a flat-line graph since every volume (assuming homogenous and isotropic) should have the same number of galaxies, and each ‘slice’ of volume should have a more-or-less the same redshift for all the readings within it. Am I missing something or is this a result of targeted observations which will not (yet) fill up the graph?

Fiddling (a little bit) with settings on @mikehelland ’s web page I feel like it should give a flatline graph at least for some sections where there have been multiple observations. No matter how I fiddled, I cannot get the flatline.

I get the distinct feeling this is showing a black body spectrum (reversed?) as much as it is showing a sample spread. A few more higher redshift readings are available than this graph above (likely more recent and from JWST), giving an initial impression that with technology we would fill up the graph with new observations.

If the ‘blackbody’ concept holds water then the very distant galaxies will remain obscured, for reasons to be investigated. We may find a few but we will never fill that graph to the top.

Coming back to ‘H’ I can somehow concur with @budrap00 that working with H pledges an allegiance to the SMC, since the units of H is essentially 1/seconds. This is also where the concept of t=0 comes from and immediately lends itself toward thinking of a BigBang at t=0. Using H biases the user of it to think as redshift of an evolution over time, and disqualifies ‘other thinking’. Yes, this is fixed when we use it in the form $c/H$ but the biased thinking remains, and redshift over distance remains cough blasphemy.

Mike you mentioned in an earlier post that you had a different idea but then abandoned it. It appears at first glance this idea could also have been pointing you at a ‘redshift over distance’?

@Francois-Zinserling

Awesome job loading up that tool and playing around! The settings that I find most interesting are very close to yours, except at -24 instead of -25 magnitude:

It gets close to a straight line, albeit, not flat.

Note that these are not galaxy counts. They are quasar counts. Either this data is accurate, which heavily implies that quasars were unique to the early universe and are going extinct now (and thus evidence for an expanding universe), or something about how we’re measuring and classifying these quasars is amiss.

If the quasar is closer to home, and we can see it better, it usually gets classified as an AGN instead of a quasar.

I’ve found in the SDSS Q16 paper that the previous release had some bugs. I think maybe they double-dipped the continuum when making the K-corrections. Lots more info in #210 and #260 .

For galaxy counts I’ve used the DESI early release data and got this:

Bright galaxies (BGS) in the redshift (z) range 0.05 < z < 0.4
Luminous Red Galaxies (LRG) for 0.4 < z < 1.0
Emission Line Galaxies (ELG) for 0.6 < z < 1.6
Quasars (QSO) for 0.9 < z < 2.1

Here is what the data looks like altogether:

H pledges an allegiance to the SMC, since the units of H is essentially 1/seconds.

Note that H is basically a frequency.

This is also where the concept of t=0 comes from and immediately lends itself toward thinking of a BigBang at t=0.

Suppose the universe doubles in size ever 10 billion years. That means, going backwards, it halves in size every 10 billion years. As t approaches -infinity, the size approaches 0, but it never actually gets there at any finite time.

That is an exponentially expanding universe, known as a de Sitter universe, or a “pure dark energy” universe, i.e., $\Omega_m = 0, \Omega_\Lambda = 1$.

In such a universe there is no t=0 or big bang singularity. To get that from the model you have to include matter.

It’s always a pleasure to trigger someone who is passionate about this stuff :)

It would appear that we are not going to get a flat line, if the numbers above are anything to go by. BGS >> all the rest ELG > LRG which is awkward since z(ELG) > z(LRG) on ave.

Any idea why ELG has a hole at 0.5? Even in the sum total there’s still a dip.

On the other hand ESO appears to have the correct curve, which might flatten out a bit if scaled by volume? Again, it only goes up to ~4, and new data comes out for z>>4 because that’s where people are looking, but it means there will be a new bump further down the curve.

I know the above is due to specific samples/instruments/satellites and methods, which is somewhat already evident in the ‘cosmology crisis’.

Re: t=0: The BB gang had the same problem when counting back to 0, which in reverse means the universe would have needed an infinite time to expand to something worthwhile, or couldn’t even do that if it started at size=0. So they invented inflation. I mean … why not? We have quarks so why can’t we have inflation? No crisis needed here!

The difference being then that after inflation, the Big Bang basically happened everywhere. This gives the BB a bit more credibility, except not.

Any idea why ELG has a hole at 0.5? Even in the sum total there’s still a dip.

Not really. These are the z ranges provided for each category:

• Bright galaxies (BGS) in the redshift (z) range 0.05 < z < 0.4
• Luminous Red Galaxies (LRG) for 0.4 < z < 1.0
• Emission Line Galaxies (ELG) for 0.6 < z < 1.6
• Quasars (QSO) for 0.9 < z < 2.1

Why don’t they do all types from z=0 to z=2? Resources, I’m sure. Providing results on a reasonable time frame I suppose.

So, let’s look at the distances on Louis’ calculator. z=2 is 14.5 Gly. A sphere with that radius has a volume of 12,770 Gly^3.

Let’s divide it into 10 equal volumes of 1,277 Gly^3, find the radii to get each volume, and use the calculator backwards to find z:

z       Gly  
0       0  
0.665   6.730  
0.90    8.480  
1.09    9.71  
1.24    10.68  
1.39    11.51  
1.52    12.23  
1.65    12.87  
1.76    13.46  
1.88    14.00  
2       14.5

This is saying, in that model, there should be the same amount of galaxies from z=0 to z=0.665 as there are from z=1.88 to z=2.

Agreed?

Now let’s use z=20:

z       Gly
0       0
3.1     18.66
        23.51
        26.91
        29.62
        31.90
        33.91
        35.70
        37.31
18      38.81
20      40.20

There should be as many galaxies with z<3.1 as there between z=18 and z=20.

I was about to whole-heartedly agree when I recalled your equation

$d=(z/(1+z))*c/H$

Which provides a relation of distance to redshift in a non-expanding space - in your model, right? This is not a widely accepted equation, or is it? I tried looking for equations in an expanding space and AI kept telling me I’m not smart enough to understand it. It’s right of course, but how does it know!?

Is the above (volume) bands back-calculated from this equation? If yes, then, I agree the result should be similar counts of galaxies in all those volumes. Finding this would be a strong support for the model.

Not finding it does not kill it but then we might have to question other theories e.g. homogenous and isotropic throughout the cosmos. Also, it is very dependent on the samples so far. I don’t know if there have been other studies trying to relate ‘number of galaxies’ per volume, and the data may be skewed if the studies had different goals. E.g. a study of “look for galaxies 2<z<3” would provide a blob of samples that makes it look like there are more galaxies in that range. Although if you can split 2<z<3 into 20 volumes and find a flat line there you’re in the pound seats.

@Francois-Zinserling . >This is not a widely accepted equation, or is it?

The equation is a known result. Take a look at “Radiation alone” as copied from this reply in Why “z” for redshift, and d = zc/H in particular should be rejected in a non-expanding universe.

@Francois-Zinserling . >AI kept telling me I’m not smart enough to understand it.

Let’s have a few quotes from Velocity dependent inertial induction and Gravity Probe B?

• One:

Who says that the “able to cope” can be judged by an AI machine? You know, computers are Nonsense Amplifiers most of their time.

• Two: >AI can only parrot the mainstream.

Simple and straightforward. It’s in the mainstream that common people are not smart enough to understand their Sophisticated Physics.

• Three:

A dimensions check reveals that your AI may be Artificial but not very Intelligent.

Not being smart enough? Do you still accept that a dumb machine is teaching you that sort of a lesson?

The “widely accepted” solution for angular diameter distance in FLRW/LCDM is this: https://people.ast.cam.ac.uk/~pettini/Intro%20Cosmology/Lecture05.pdf

When $\Omega_m=0$ and $\Omega_\Lambda=1$ that simplifies to my equation.

I didn’t know any of that when I “found” it though.

Basically I had done some simulations and graphed some results. It was only when comparing it side by side to known cosmologies (in this case, de Sitter) did I see my results were the same as that given by that equation. From there I was able to derive it from Hubble’s law and the definition of z redshift.

So, we have my equation, that leads equal volumes of space having larger and larger z ranges as you go out, e.g., the observable region split into 4:

• 0.0000 < z < 1.7024
• 1.7024 < z < 3.8473
• 3.8473 < z < 9.9362
• 9.9362 < z < infinity

And then you have Tired Light and the expanding universe models that say equal volumes get smaller and smaller ranges of z as you go out:

z       Gly  
0       0  
0.665   6.730  
0.90    8.480  
1.09    9.71  
1.24    10.68  
1.39    11.51  
1.52    12.23  
1.65    12.87  
1.76    13.46  
1.88    14.00  
2       14.5

(In Louis’ calculator, the angular diameter distance of his model is usually pretty close to the comoving distance in the standard model.)

I think based on what’s been observed so far, the former is a better bet than the latter.

@HanDeBruijn

Take a look at “Radiation alone”

Also take a look at $\Lambda$ alone, and consider that angular diameter distance is comoving distance divided by $1+z$. You can get my equation that way too.

Most of the papers it cites are April Fools papers too.

For the above samples, do you know how sampling was done, e.g. for BGS 668667 samples - is that the sum total of ‘all they could find’ or is it a ‘ok we have enough now’? The latter may not be a big help with your galaxies per volume calculations.

From my understanding, this is 10% of what DESI will be releasing. So, that’s fun. Here’s more detail if you want to take a look and break it down for us:

https://ui.adsabs.harvard.edu/abs/2023AJ….165…50M/abstract

Here are the graphs over my bins $\frac{z}{1+z}\frac{c}{H}$

The standard bins are in 0.1 increments from z=0 to 4. So I calculated 40 equal volumes from z=0 to 4 using my equation like this:

divideBy = 40
R = 13.8
V = 4/3 * np.pi * R**3

# z=4 is 80% of R
Vz4 = 4/3 * np.pi * (R * 0.8)**3
print(Vz4 / V)

V_40 = Vz4 / divideBy
for n in range(divideBy):

    r = (n * V_40 / (4/3 * np.pi))**(1/3)
    z = 1 / (1-r/R) - 1
    bins[n] = z
    print(z)

As for Louis’ SSTz calculator, I incorporated that into my FLRW graphing calculator to compare them side by side. You’ll see radial distance in SSTz tracks pretty close to comoving distance in FLRW.

https://mikehelland.github.io/hubbles-law/other/flrw_sstz.htm

According to that calculator, z=4 is 21.3 Gly away. So calculate the volume to that, divide it by 40, and find the radii for each equal volume.

#SSTz values
#z=4   21.3 Gly    40,479 Gly^3

Hz = 0.247

R = 21.3
V = 4/3 * np.pi * R**3
V_40 = V / 40
print(V_40)
for n in range(divideBy):
    r = (n * V_40 / (4/3 * np.pi))**(1/3)

    log1z = r  / 3.261564 * Hz
    
    bins[n] = np.exp(log1z) - 1
    print(bins[n])

And that gives us this:

Note that, because the bins aren’t linear over z, they’re shown on these graphs as different widths. That’s a bit misleading. You should be considering the big fat bar at z=0 to be the same width as those further out.

@mikehelland for small redshifts $z<1$, $\quad \frac{z}{1+z} \frac{c}{H_0}$[SSTz] is close to $\frac{c}{H_0} ln(1+z)$. But the bin size on your graphs, for $z<1$, is much larger for SSTz, by a factor 2 or 3.

Is it because you picked $z=4$ as a reference, which is a greater distance for SSTz than for $z/(1+z)$?

@mikehelland never mind, I just saw your latest post !

Yeah, much more observation and analysis is needed. But on the surface, the two distance equations give very different pictures of the universe at large.

Instead of z=4, let’s now think about out to z=20. And instead of 40 equal volumes, let’s consider 200 equal volumes.

The last ten bins out of 200 in SSTz are:

18.941 19.045 19.15 19.256 19.361 19.466 19.572 19.678 19.784 19.89

The last two bins according to z/(1+z) is:

18.683 19.321

In other words, from about z=19 to z=20, SSTz predicts there are ~10x as many galaxies as z/(1+z) in the same range.

The low counts around z = 0.5 may just be due to a lack of spectral lines within the wavelength range of the spectrometers. What if that’s also happening for z > 2 ?

The Bright Galaxy Survey actually has more galaxies in it than the others by a lot, and they’re all within z<0.5.

DESI basically is looking for galaxies z < 1.7, so only the quasars are really looked for beyond that.

https://www.desi.lbl.gov/2022/01/12/selecting-targets-for-the-desi-survey/

Actually, a lot more than 10x I think.

Each of the bins for SSTz should have the same number of galaxies as there are between z=0.0 and z=0.683.

Each of the bins in z/(1+z) has the same as between z=0 and z=0.195. Here are the first dozen or so bins.

0.0 0.195 0.258 0.307 0.349 0.386 0.42 0.452 0.483 0.512 0.541 0.568 0.595 0.621 0.646 0.671 0.696 0.72

So, since the bins in SSTz have ~15 times as many galaxies as the z/(1+z) bins, and there are ten times the bins from z=19 to z=20… SSTz predicts ~150x as many galaxies in that range.

@mikehelland Of course the two distance equations give a very different view of the universe since they are derived from two very different views of the universe!

Counting galaxies in a volume is subject to a very strong Malmquist bias. However, looking at galaxy diameters is less sensitive to such bias because it is based on galaxies we can see (although still not perfectly immune to biases).

$(c/H_0) \times z/(1+z)$ asymptotically converges to $c/H_0$ at large $z$. Could you plot it on this figure from Lovyagin Fig. 5?

On the graph, “TL = SSTz” is from $\ln(1+z)$, the orange line is $z/(1+z)$ (please confirm…)

Yeah, there is no angular diameter turnaround, so that orange line would be right. Unless for some reason time dilation affected the angular diameter.

$z \lesssim 30$ they say? With (my version of) the Variable Mass Theory cosmological redshift cannot become higher than $z_{max} \approx 28.5$ . I’m breathlessly awaiting ..

Given current photometric “galaxies” at z=25 I assume redshift saturation at 28 is likely falsified, moreover the CMB itself likely has a true redshift of 1100 I do appreciate the idea of solving Olber’s paradox through hidden redshift, hence the interest in 30mhz astronomy (via a moon telescope), indeed there has been hints of a radio background excess https://academic.oup.com/mnras/article/521/3/3939/7079142

https://arxiv.org/abs/2504.20664

@LifeIsStrange . >moreover the CMB itself likely has a true redshift of 1100

Which is typical for the Big Bang model. In static models the CMB is caused by entirely different mechanisms and it has NO such true redshift. A closer look at dark photon explanations of the excess radio background. Ah! Dark photons! Still another sort of “new physics” emerging. I would like to shout to those geniouses: Please, finally, show some restraint!

Again on the excess radio background I stumbled on this new paper https://arxiv.org/abs/2505.00373

The 68 per cent credible interval suggests an excess radio background which is more than 100 per cent of the CMB at 1.42 GHz, while the 95 per cent credible interval of the radio background efficiency parameter spans the entire prior range. The behaviour of the credible intervals is similar at all redshifts

This means the excess radio background contains twice as much photons as the CMB? I’ve read the CMB contains 50% of all the photons that have ever been emitted in the universe hence hence this means the radio excess contains AS MANY PHOTONS THAN THE WHOLE UNIVERSE. Is there something I’m missing??

Submitted to the Open Journal of Astrophysics. Read this https://telescoper.blog/2025/05/19/a-galaxy-at-redshift-z14-44/ Naidu and team have written good papers in the past. This one has not been reviewed yet, but the spectrum is convincing enough to me.

@RedshiftDrift : the maximum redshift in VM is 28.5 . And there is nothing I can “improve” on it.

And there is nothing I can “improve” on it.

And that’s a big advantage VM has over ΛCDM!

The MIRI spectrograph on JWST can detect some light up to 12 μm with a resolution of 100. With enough ‘exposure’ this should be enough to see the Lyman-α line at z ≈ 100. Hoping that astronomers will try to get the spectrum of Capotauro in the near future. Of course, there is always a possibility of a bad interpretation of spectra, especially from an object this far, so VM won’t be falsified any time soon.

@RedshiftDrift thanks for sharing, it might be an interloper but anyway this could be BIG