a-cosmology-group/acg#385

@Francois-Zinserling writes: >Anyone might come with an alternative for the CMB [ .. ]

Here is the work ACG has done on the CMB. And this has been my best shot at the CMB so far.

$$ u_{CMB} = \frac{4\sigma}{c}\Theta^4 = \frac{W.\mbox{VMT}.e^{-W}}{32\pi.w}\frac{(Hc)^2}{G} $$

Apart from details, the idea is that the CMB energy density at our position is divided by the maximal intrinsic redshift of the energy density at the rim of the Observable universe, which is given by $1+z_{max}=e^W$. This would lead to a enlargement of the temperature $\Theta$ itself by an factor of $e^{W/4} = (1+z)^{1/4}$. However, according to the video by Gareth this factor must be $(1+z)$ instead. Theoretically, the latter is in concordance with Wien’s displacement law, as follows.

$$ \lambda_{peak} = \frac{b}{\Theta} \quad \Longrightarrow \quad \frac{\Theta_O}{\Theta_0} = \frac{\lambda_0}{\lambda_O} \quad \Longrightarrow \quad \Theta_O = (1+z_{max})\Theta_0 \approx e^{3.383634283}\times 2.726\mbox{ }K \approx 80.356\mbox{ }K $$

where $\Theta_0$ is the CMB temperature here and now and $\Theta_O$ is the CMB temperature at the rim of the Observable universe. It all means that my best shot at the CMB is plain wrong. Not unexpectedly, because the formula has been found by matching and stretching, while knowing the CMB temperature at our place. But anyway, it’s useful to have an estimate for $\Theta_O$ now. (Does everybody see the difference between $0$ and $O$ ?)

It is seen that our maximal redshift as well as our maximal temperature is inside the range of the data displayed in the two screenshots. And because of the logarithmic scale for Redshift in the second picture the temperature rises there as an exponential.

@Francois-Zinserling writes: >it is my opinion that the ‘rim of the observable universe’ is just one telescope away from being extended.

The ‘rim of the observable universe’ has a very special (and perhaps rather counter-intuitive) meaning in the Variable Mass Theory (VM). It is e.g. the same for any observer, and its distance is

$$ R_O = W.\frac{c}{H} $$

where $W=3.383634283$ , $c=$ lightspeed in vacuum , $H=$ Hubble parameter .

I am not going to repeat the whole story at this place.

As for the rest of your argument: I just can’t make sense of it. So let’s repeat.

It seems to me that the labeling of the temperature axis is somewhat sloppy. I would expect a subdivision in the decimal system, which is likely not (?) the case. (Is it a subdivision in units of 5K ? Then where is the 2.7 K at the origin ? ) But let us concentrate on the axis labeled “Redshift”. I think it is not really the redshift but (one plus the redshift) instead: $z \rightarrow (1+z)$. And the real variable at that place is not even $(1+z)$ but $s=\log(1+z)$, which is the definition of a logarithmic scale $s$. Now look at the formula for CMB temperature.

$$ \large s=\log(1+z) \quad \Longrightarrow \quad 1+z = 10^s $$

$$ \large \Theta(z) = (1+z)\Theta_0 = \Theta_0 10^s \quad \mbox{with} \quad _0 = \mbox{here and now} $$

Meaning that the linear relationship for $\Theta$ in $z$ looks like an exponential at the logarithmic scale $s$ . For $z=0$ we simply have the CMB temperature at our place: $\Theta(0) = \Theta_0 10^s = \Theta_0 10^{\log(1+0)} = \Theta_0 10^0=\Theta_0$.

Meaning that the linear relationship for Θ in z looks like an exponential at the logarithmic scale s

I think this is a good reminder of what the graph actually represents. Meaning my ‘it looks like a reverse exponential decay’ is a result of the scale, and my whole point thus moot. 🤣

@Francois-Zinserling . Yesterday it looked better than it looks now.

Your whole point may be moot. But my scale is not good :-(

Update

The picture according to the above would be something like this

which is similar but not quite what’s in the video.

@RedshiftDrift and @ExpEarth .

From Can the CMB temperature be less than 2.7 K ? (broken) this picture:

And another picture from this reference:

The measurements of the CMB temperature in diffuse interstellar medium of the Milky-Way and high redshift galaxies based on excitation of C_I fine-structure and H₂ rotational levels

So what is it ? Is $\Theta(z) = (1+z)\Theta(0)$ indeed linear in the cosmological redshift ? Or is the CMB temperature an absolute constant ?

You most likely have it right with the first answer, T(z) = T0(1 + z) . Gareth had this relation as #4 in his list of things alternative models have to explain. He concedes that there could be errors in the techniques, as @RedshiftDrift has also argued, but at this point the burden is on others show where the measurements are wrong. The relation was used to draw my figure above. It totally fits with the shell universe model, where we have the radiation from the hot shell being redshifted as it goes to the centre. There’s a corresponding blueshift in radiation going outwards towards the shell. For an observer at the shell, the centre of the universe would look ver bright. The relation seems to somehow fit your model too, but I can’t say for sure, as I still don’t understand your model.

@ExpEarth . >as I still don’t understand your model.

Don’t bother, Matt, because as concerning the CMB I do no longer understand it myself too :-( Note. With Variable Mass (VM), $T$ is systematically replaced by $\Theta$ for temperature, because $T$ has been reserved for Orbital time.

14:44 “…how incredibly difficult it is to construct an alternative cosmology”

I think that about sums it up. Thankfully LCDM did not have all ‘green’ tabs though.

I tried to do a similar analysis… then gave up after reading 75 alternative cosmologies!

@RedshiftDrift

Apart from your model and the New Tired Light (which I know you view positively), which models do you think are the least problematic among the ones you’ve examined? Which ones do you think could potentially be salvaged and made to work well with enough modifications or revisions?

As things stand now, I wouldn’t call your model an actual cosmology. You’ve developed a very solid explanation for redshift, but you’re still working on your paper about the CMB, and you still need to develop more refined explanations for galaxy rotation curves and the other phenomena currently attributed to dark matter. So I’d describe your model more as an emerging cosmology, something that’s gradually taking shape.

@luisenrique-arch you are right, the STz framework and NTL are not cosmologies.

None of these cosmologies can be salvaged! Instead, the next cosmology will come from parts of the proposals made by Ashmore (FRBs), Brynjolfsson (distance relations), Lerner (plasmas), and Narlikar/Hoyle/Burbidge (nucleosynthesis), with STz as an explanation for redshift, light-curve stretching, and the CMB.

@RedshiftDrift writes: >with STz as an explanation for redshift, light-curve stretching, and the CMB.

(1) redshift is also explained by the Variable Mass theory, which is incompatible with Tired Light (2) light-curve stretching is also described by the Time Dilated Past hypothesis, compatible with VM (3) and the CMB is still a nightmare which so far as I know is shared by all of us in A Cosmology Group

@HanDeBruijn

If the CMB is a nightmare for many of the cosmological models proposed by members of this forum, as you yourself admit, then why do you all put so much effort into trying to find alternatives to the Lambda-CDM model, which actually explains the CMB very well?

Please, don’t take my question as a provocation. I absolutely agree we should be looking for alternatives to Lambda-CDM. I’m not trying to argue that Lambda-CDM is correct. I’m asking this question simply because I want to understand where you guys are coming from, and why you think it’s worth pursuing these alternative models despite the difficulties they have with the CMB.

@luisenrique-arch . >why do you all put so much effort into trying to find alternatives to the Lambda-CDM model

What would you do, if you have to choose between Chronology of the universe or Genesis 1 ?? I made my choice about ten years ago. I’m an old earth creationist, if you want to put me in a box.

Yes @HanDeBruijn the CMB is a tough nut to crack. But I’m working on it from the point of view of STz (what else :smile:) and it’s promising. @luisenrique-arch I still think that the CMB is produced by an equilibrium between STz redshift and Sunyaev-Zel’dovich blue-shift; that’s one of the many reasons why I think it’s worth pursuing this alternative explanation. (STz is not a model…)

@RedshiftDrift

STz is not a model…

Well, it’s not a cosmological model, but it’s a redshift model.

This reply is the last in a series of one , two , three , four .

Elsewhere, the following formulas for the Hubble parameter $H$ have been found.

$$ H^2 = \chi G \rho_c \quad \mbox{with} \quad \chi = 8\pi \times \begin{cases} 1/8 & (: \mbox{OI}) \ 1/6 & (: \mbox{Mach}) \ 1/3 & (: \Lambda\mbox{CDM}) \ w & (: \mbox{VM}) \end{cases} $$

where $G=$ gravitational constant, $\rho_c=$ critical mass density of cosmos, $w=$ 0.3883945571 dimensionless constant. The first and the second case will be ignored in the current context, leaving us with the cases (ΛCDM) and (VM).

In the Variable Mass theory there is not a single value for the Hubble parameter, because $H=(2/A)$ where A is an “Age” and A can even be the age of the earth. To put it even stronger:

with VM the Hubble tension is real and required !!

Let us first define the Hubble parameter of the Observable universe in VM:

$$ H_O^2 = w.8\pi.G.\rho_c \quad \mbox{(Late universe)} $$

And a different Hubble parameter for the Cosmic Microwave Background:

$$ H_{CMB}^2 = \frac{1}{3}.8\pi.G.\rho_c \quad \mbox{(Early universe)} $$

Then it follows that

$$ H_{CMB}^2 = \frac{1}{3w} H_O^2 \quad \Longrightarrow \quad \boxed{ H_{CMB} = \frac{1}{\sqrt{3w}} H_O } $$

Numerical values are obtained at hand of the following data. >‘Hubble constant – at 67.4 (+/- 0.5) km/sec/Mpc’, NASA Science, July 22, 2018 ‘Hubble constant at 73.2 (+/- 1.3) km/sec/Mpc’, The Astrophysical Journal Letters, February 2021

$$ H_{CMB} = \frac{1}{\sqrt{0.3883945571\times 3}} \times 73.2 = 67.8 $$

which is according to the data !!

This confirms that we must indeed use the ΛCDM entry in the above picture. Leading immediately to the desired result, as displayed with bold font in our last reply:

the outcome is Θ₀ = 2.725 K , which accurately equals the empirical value

@RedshiftDrift writes: >I still think that the CMB is produced by an equilibrium between STz redshift and Sunyaev-Zel’dovich blue-shift

Oh no, Louis, I think it’s not by far that complicated, but let Occam’s razor decide. Meanwhile I will be preparing a ground-breaking paper for QSSC that nobody is interested in :-(

Update

Check, check, double check with MAPLE.

W := 2.096433787;
II := exp(4*W)*(W^2/4-W/8+1/32)-1/32;
G := 6.67408*10^(-11);
c := 299792458;
sigma := 5.670374419*10^(-8);
Mpc := 3.08567758*10^22;
H := 67.4; # Early
H := H*1000/Mpc;
M_O := c^3*W/(2*G*H);
Theta_0 := (M_O*c^2/4/(4*sigma/c*4*Pi*(c/H)^3*II))^(1/4);
Theta_0 := evalf(Theta_0);
H := 73.2; # Late
H := H*1000/Mpc;
M_O := c^3*W/(2*G*H);
Theta_0 := (M_O*c^2/4/(4*sigma/c*4*Pi*(c/H)^3*II))^(1/4);
Theta_0 := evalf(Theta_0);

Giving respectively $2.61(2)\mbox{ K} \le \Theta_0 \le 2.72(2) \mbox{ K}$. 🤔