Cosmic Potential Theory (CPT): Cosmology without the Big Bang or dark matter

[luisenrique-arch]

Cosmic Potential Theory (CPT): Cosmology without the Big Bang or dark matter

by Peter Wolff

Translation by lluisenrique-arch

Overview: Classical gravitation, both in Newton’s formulation and in Einstein’s General Relativity, is fundamentally a local theory. It does not, by itself, make precise claims about an infinitely extended universe unless additional assumptions about the global structure of the cosmos are introduced. A key but often implicit assumption is that a perfectly isotropic, infinitely extended spherical shell of mass surrounding any finite and observationally accessible region of the universe produces no net gravitational field inside it. This is strictly true for finite isotropic shells in both Newtonian gravity and General Relativity, as expressed by Birkhoff’s theorem. The implication is that, on very large scales and under isotropy, gravitational fields are determined only by local distributions of mass and energy. However, the Einstein-Mach principle suggests something different. It proposes that inertia, which in Newtonian physics is simply postulated, is actually induced by the total distribution of mass in the universe, including extremely distant matter. This idea, however, is not fully supported even within General Relativity, as illustrated for example by the Gödel universe model.

The Newton-Mach Principle (modified): Here we define a modified version of the Einstein-Mach idea. In this formulation, inertia is determined exclusively by the infinitely extended isotropic mass shell described above, while finite distributions of matter play only a negligible role. The advantage of this modification is that an actually infinite mass shell can, unlike a finite one, provide a physical foundation for Newton’s concept of absolute space, or at least make it plausible. On sufficiently large cosmological scales, only this infinite and isotropic mass shell is relevant. Local structures, which are anisotropic, finite and inhomogeneous, contribute only secondary corrections that vanish as the density ρ approaches zero.

Core idea of modified cosmic gravity: In an idealized homogeneous and isotropic universe extending infinitely, filled uniformly with matter, classical Kepler-Newton gravity appears not as a purely conservative force but as a kind of cosmological dissipative acceleration that slows down test masses. For light, this effect is constant because the speed of light in vacuum is locally constant and equal to c. The source of this cosmic gravitational effect is the infinite isotropic mass shell that encloses any finite observable region of the universe. Local masses within a finite region around the observer do not directly determine this global acceleration. They influence it only indirectly by shaping local gravitational fields, which can slightly redirect the global effect. This leads, in galactic dynamics, to behavior similar to MOND theories. This framework introduces a universal deceleration scale proportional to Hc, where H is related to cosmic parameters. This plays a central role in the Cosmic Potential Theory (CPT).

The static cosmology core of CPT: In standard Big Bang cosmology, the Hubble expansion is interpreted as a real expansion of space that is accelerating. In CPT, a different interpretation is proposed. Using a kind of mathematical reinterpretation based on Einstein’s equivalence principle (1907), particularly the elevator or rocket thought experiment, it is assumed that light traveling toward us is actually being gradually decelerated by gravity. At the same time, we interpret observations as if we were moving away from the light source with constant acceleration. This dual interpretation reproduces the observed redshift without requiring cosmic expansion. In this sense, the debate resembles the historical opposition between Aristotelian-Ptolemaic and Copernican-Aristarchian cosmologies. In CPT, it is not the universe that expands and accelerates. Instead, light is progressively “slowed down” or “aged” by cosmic gravitational effects.

Consequences for Hubble expansion and dark energy: The observed accelerated expansion since 1998 is interpreted in CPT as strong evidence for this framework. Within standard cosmology, the data require acceleration to fit supernova observations, but this acceleration has no intuitive physical explanation. Dark energy is introduced in standard models as an additional unknown component. In CPT, it is instead viewed as a placeholder for an unexplained interpretation of observational data within an expanding-universe framework.

Hubble constant and cosmic density: In CPT, the Hubble constant H is related to the average density of the universe ρ, which is not directly measurable on the largest scales. A plausible approximation assumes that the density ρ₀ measured on the largest accessible scales is close to the true cosmic density ρ. This yields:

H² = (8π/3) G ρ ≈ (8π/3) G ρ₀

where G is the gravitational constant. In this framework, H does not represent an expansion velocity. Instead, it represents a cosmic deceleration scale that affects light propagation and produces redshift effects without requiring expanding space.

Cosmological constant and dark energy: The cosmological constant Λ, associated in standard cosmology with dark energy, emerges in CPT as:

Λ ≈ (3/c²) H²

In standard physics, Λ is poorly constrained and can differ from theoretical vacuum energy estimates by 60 to 120 orders of magnitude depending on assumptions. In CPT, Friedmann models are not fundamental but instead act as parameter-fitting frameworks. Similarly, dark matter is not required as an independent physical substance but as a modeling parameter introduced to reconcile theory with observations.

Space-time structure in CPT: CPT describes space-time as a reinterpretation of Special Relativity combined with a Newtonian-like absolute reference frame. This frame is defined with respect to the cosmic microwave background and distant galaxies and quasars, similar to a Poincaré-Minkowski inertial frame at rest relative to the universe at large. On cosmic scales, rest and motion are distinguished physically by the presence of a gravitational deceleration field. This leads to:

• A globally static universe
• Cosmological redshift
• Gravitational time dilation

MOND-like galactic dynamics: One of the strengths of CPT is that it naturally produces behavior similar to MOND (Modified Newtonian Dynamics), including flat galactic rotation curves and the Tully-Fisher relation. When gravitational accelerations fall below a characteristic scale a₀ ≈ Hc, Newtonian dynamics begins to deviate. This transition emerges naturally from including cosmic deceleration in gravitational dynamics. The MOND scale is therefore not an independent empirical constant but arises from cosmological structure itself.

Cosmic microwave background: In CPT, the cosmic microwave background is interpreted primarily as highly redshifted and thermally equilibrated starlight. Because the universe is assumed to be static, there is sufficient time for radiation to thermalize into a near-perfect blackbody spectrum. Remaining anisotropies are attributed to matter distribution and foreground effects, such as the Sunyaev-Zel’dovich effect. Importantly, unlike classical tired-light models, CPT preserves the blackbody nature of the spectrum.

Supernova observations: CPT claims to reproduce supernova type Ia luminosity-redshift relations without free parameters, relying instead on cosmic density and H. These results are presented as being competitive with or superior to standard cosmological models, which require dark energy and additional adjustable parameters.

Additional assumptions: To complete the framework, CPT introduces several supplementary hypotheses:

1. Super-dense masses: True black holes may not exist in a static universe. Instead, extremely compact objects near the Schwarzschild radius could mimic black hole behavior.
2. Mass-element cycles: A continuous recycling of matter is required in a static universe.
3. Small-scale explosive processes instead of a Big Bang: Active galactic nuclei may eject matter over large distances, contributing to cosmic matter recycling. In a more speculative form, repeated small-scale energetic events could replace the need for a single initial cosmological origin event.

Original source: https://www.wolff.ch/astro/it/index.htm

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What I translated is only an introduction that the author of the theory wrote on his website back in 2008. Here you can find the full paper, where the entire theory is laid out in detail:
https://www.wolff.ch/astro/ur.pdf

Unfortunately, the paper is written in German, so you’ll have to translate it little by little

[RedshiftDrift]

In Peter Wolff's original paper "Kosmologie ohne Urknall und dunkle Materie", his modified Newton-Mach Principle appears not as a purely conservative force but as a dissipative acceleration. As for all dissipative processes, the solution is an exponential described by the Beer-Lambert law.

Wolff solves the equation (once again) to get an energy loss that follows a $\ln (1+z)$ function:

"Daraus kann man $\tau(z)$ unter Benützung von $dt = dz/H$ aus (1) ausrechnen:

$$ dτ = dt/(1 + z) = 1/(1 + z) dz/H \mbox{ und daraus } τ (z) = ln(1 + z)/H \quad \quad \quad \quad \quad (2) $$

Dieses $\tau(z)$ kann man als die Eigenlaufzeit der "Lichtspuren“ z.B. in Absorptionslinien von gravitativ rot verschobenem Licht ansehen"

Ok good, red-shifted light comes out of that dissipative gravity! We know this is the correct Hubble function (e.g. https://doi.org/10.3390/galaxies10060108) for the angular distance. However Wolff's model doesn't explain anything beyond that. How is the CMB explained? (His explanation as "thermalized starlight" has been proposed by others and was falsified.) Why is the MOND acceleration equal to $\sim 10^{-10} \mbox{ m/s}^2$? Why are wide-binaries not following the expected MOND behaviour? How are galaxy-quasar associations explained? The Earth's orbit around the sun does not dissipate energy and which shows that gravity is a not a dissipative force!

"Cosmic Potential Theory" is another example of a theory invented to solve a specific problem, but it doesn't answer anything else. The theory is missing predictive power and falsifiability (either observational or theoretical falsifiability).
So the whole thing is a fail 👎 👎

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I didn't know about this theory, thanks @luisenrique-arch for pointing it out. Another one I will add to my collection of "dead cosmologies".

[RedshiftDrift]

@luisenrique-arch light is thermalized in systems with high absorption, i.e. almost 100%. But we see distant galaxies at mm wavelengths, which means that the absorption cannot be high enough to produce a blackbody spectrum like the CMB.
No thermalization effect can produce the CMB.

[luisenrique-arch]

@RedshiftDrift

light is thermalized in systems with high absorption, i.e. almost 100%. But we see distant galaxies at mm wavelengths, which means that the absorption cannot be high enough to produce a blackbody spectrum like the CMB.
No thermalization effect can produce the CMB.

So what do you think is the cause of the CMB?

[RedshiftDrift]

The CMB is radiation in equilibrium between STz redshift and Compton scattering. That is explained in a paper I submitted in December and is still under review...

[Francois-Zinserling]

@RedshiftDrift

submitted in December and is still under review...

Is this normal?

I submitted in early January. Still under review (no decision to publish yet) and I am already thinking this is taking too long!

[RedshiftDrift]

@Francois-Zinserling It's not normal for the journal I submitted it to. They claim a decision is reached after an average of 40 days...

[LifeIsStrange]

The cmb temp evolve with redshift (1+z) this pose a fine tuning problem to the age/steady state of light.
The CMB cannot just be star light but refshifted with considerable time because an universe with this age would unless I am mistaken, lead to an even higher cosmic radio background than the cosmic microwave background.
While there is a CRB excess, it contains far less photons than the CMB.
One might assume giant subdecametric luminosity but nothing would explain the gap between radio and sub observable radio.

[HanDeBruijn]

@RedshiftDrift writes:

I already have more than two home runs with this!

Whoa, Louis, not so fast !!

I already have found the 'correct' redshift mechanism, it predicts the observed $d=c\mbox{ }\ln(1+z)/H_0$ law

Sure, and e.g. the Variable Mass (VM) theory predicts exactly the same.

predicts the value of the Hubble constant from the electron density in the IGM

• The Variable Mass (VM) theory - on the contrary - predicts that there always will be Hubble tensions.
  There is even a Hubble parameter which is twice the inverse of the Age of the earth, according to $H=2/A$ .
• The electron density in the IGM is almost nil. Competing TL theories predict different values for it.
  Still an issue are the (literary) incredibly high temperatures of $10^{11}$ Kelvin in that almost vacuum.
  It may be questioned if the notion of IGM temperature is überhaupt a physically meaningful concept.
• Counter arguments to counter propagation have been presented in Stimulated Transfer redshift (STz).
  I do not understand how telescopes on earth can let counter propagating beams travel towards a galaxy.

describes the CMB as the same everywhere (with a temperature I am in the process of calculating from first principles)

We are breathlessly awaiting.

an acceleration constant that happens to equal $2\pi$ times the MOND acceleration (i.e. MOND is not fundamental)

Yes but, as far as I can see, your factor $2\pi$ comes out of the blue sky; it is not really calculated.

explains the galaxy-quasar associations discovered by Arp,

Yes, and the Variable Mass Theory, as designed by Arp and Narlikar, does of course the same.

And our own version of VM does a lot more.

With part I of the Variable Mass theory, as published here, at least three predictions on an earthly scale can be made:

• The shrinking kilogram is 52 micrograms theoretically, about 50 micrograms empirically
• The Earth's Rotation Retardation is $5\times 10^{-22}$ rad / $s^2$ theoretically, about $6\times 10^{-22}$ rad / $s^2$ empirically
• Leap seconds are 69 seconds per century theoretically, about 64 seconds per century empirically

It is noticed that three such meager experiments have been enough for acceptance of General Relativity as a mainstream theory. But the mathematics of the Variable Mass theory is childishly simple when compared with the machinery of General Relativity.

Part II of the Variable Mass theory, as published here, solves for classical gravitational paradoxes.
(BTW, your name is in that publication, Louis: read the bottom line of section 7)

More VM publications are forthcoming soon. But, unfortunately,
Anything free comes without guarantee, and without referee.

[ExpEarth]

@RedshiftDrift

I already have more than two home runs with this!

If you really hit all those homers, you will surely be MVP! Your redshift mechanism is quite complex and so I'm waiting for the video replay reviewers to check if those were fair balls or ground rule doubles. Even if you just make it on base it would be a major achievement and worthy of celebration.

@HanDeBruijn

I notice that you started a thread about your paper that didn't get much attention. I will have a look. The general approach and mathematical proficiency suggest that this could be publishable at least in journals such as Journal of Modern Physics.

[RedshiftDrift]

@HanDeBruijn Some of these objections have already been answered on this forum. (i.e. the electrons are hot so light beams are counterpropagating in the electron's frame but not in the Earth's frame.) You cannot know that the factor $2\pi$ comes out of the blue sky... The paper with the calculation in it was not published!

@ExpEarth Phenomenologically, the STz mechanism is actually very simple:
"Two photons, a blue and a red, come from opposite directions and meet at an electron. The blue photon turns around by pushing on the electron and becomes an identical twin of the red photon."
It's that simple! The rest is all deduced from this simple interaction.

You already know that Big Bang reviewers act like homer referees, rejecting papers because they challenge their 'home-field' research. Waiting for their approval is like waiting for Godot!

[HanDeBruijn]

@RedshiftDrift .

counterpropagating in the electron's frame but not in the Earth's frame

Ah, suitable framing !!

You cannot know that the factor $2\pi$ comes out of the blue sky...

I've seen it passing by somewhere (if memory serves me well) but can't find it anymore (to be honest).
But you are of course free to publish it here and now.

[HanDeBruijn]

@RedshiftDrift .
Meanwhile I have published another solution for the ($2\pi$ vs. $6$) problem: it is neither of these two !!

$$ a_0 = Hc \times \begin{cases} 1/6 & \approx 0.16667 \mbox{👎} \\ 1/(2\pi) & \approx 0.15915 \mbox{👎}\\ 1/(2W) & \approx 0.14777 \mbox{ 👍}\Huge\Longleftarrow\mbox{ !!} \end{cases} $$

$a_0=$ MOND acceleration, $H=$ Hubble parameter, $c=$ speed of light in empty space, $W=$ 3.3836 (typical for VM).

[ExpEarth]

"Two photons, a blue and a red, come from opposite directions and meet at an electron.

It starts off so simply, almost romantically, but before long we will have a score of ballet dancers and an orchestral accompaniment! The reviewers are looking for red and blue to make waves.