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:
- 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.
- Mass-element cycles: A continuous recycling of matter is required in a static universe.
- 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
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
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:
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 :-1: :-1:
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”.
Brutal, but true. Drag was one of the main reasons Fatio/Le Sage gravities were ditched.
@RedshiftDrift
I didn’t know that. How was it falsified?
@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.
@RedshiftDrift
So what do you think is the cause of the CMB?
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…
@RedshiftDrift
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!
@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…
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.
I didn’t know that the CMB temperature evolved with redshift. Isn’t this something that points towards an evolving and expanding universe?
@RedshiftDrift What do you think?
The redshift evolution of the CMB temperature is not demonstrated. This is discussed here https://github.com/orgs/a-cosmology-group/discussions/127#discussioncomment-8436941 (and in a paper I submitted in December that is still under review…)
I’ve already addressed that the CMB temp consistently evolve based on both basic atom temperature / frequency absorption (rotational vibrations based on quantum orbitals) (consistent between carbon, cyanogen, h2o, etc) and also via the S-Zeldovich effect, that is : standard physics that can be verified in the lab on earth through spectroscopy, independent of any cosmology. The SU2 gauge modified electromagnetism new physics paper cited by @RedshiftDrift is 1) unproven 2) is falsified by measurements of Neff empirical total radiation in the universe because it create a neutrino boost. https://github.com/orgs/a-cosmology-group/discussions/299#discussioncomment-16331301
To be fair CMB Neff constraints are probably cosmology dependent? Though the total extragalactic background photon count is not, nor (kinda) are neutrinos flux measured on earth. Unsure if neff can be derived via this in a cosmology and optic depth independent way.
I agree with @LifeIsStrange . Others know my views already but I will briefly mention them here again for the benefit of @luisenrique-arch . The CMB temperature gradient is a crucial feature of cosmology. It is a central part of my model of the shell black hole universe. In that model, the observable universe is a black hole in the form of a spherical shell, which holds 95% of the universe’s mass. It’s all baryonic, so we don’t need dark matter or dark energy. The CMB is just the radiation that was trapped inside the shell during the gravitational collapse that formed the shell and thermalized over billions of years. The CMB temperature is highest at the shell (about 29 K) and weakest near our position (close to the centre). The universe runs on a cycle whereby: (1) the Hubble redshift of the CMB causes gravity; (2) a reverse process flips gravity and releases energy, which re-energizes the CMB. That reverse process involves what I have called the Hubble luminosity or Lambda luminosity. Basically, all mass systems release energy at the rate dE/dt = -U H, where U is their gravitational potential energy and H is the Hubble constant. For the shell universe and black holes generally the energy released inside is also equal to the Planck (or Dyson) luminosity c^5/4G. Here is a link to my paper about it: https://www.mdpi.com/2674-0346/3/3/14 There is a discussion about it also, #256 .
I admit that all of these data leave me fairly puzzled, and I’m genuinely curious to see how @RedshiftDrift will attempt to account for them in his upcoming paper. However, I don’t think that the apparent relation between the CMB temperature and redshift should necessarily be considered a definitive dealbreaker for static models.
If big bangers are allowed to say, “Our model explains 90% of the observations, but there are still a few things we need to work out,” then staticists should be able to make the same argument. In fact, one could argue that staticists are in an even better position to say that, because they have fewer unresolved problems to deal with than big bangers do.
The paper I cited is not a “SU2 gauge modified electromagnetism new physics paper”(!?), it’s a standard spectroscopy paper: R. Hofmann and J. Meinert, “Frequency–Redshift Relation of the Cosmic Microwave Background,” Astronomy, vol. 2, no. 4, pp. 286–299, Nov. 2023, doi: 10.3390/astronomy2040019.
S-Z effects interpreted as a rise of CMB temperature only works in expansion cosmology. In static spacetime cosmology, no temperature increase is necessary to produce observations.
Your model was built to fit an increasing CMB temperature with redshift, it doesn’t explain it.
Such a temperature variation with redshift implies an event in time when the temperature was very high, i.e. the hot Big Bang. That is incompatible with a static model.
Most of what the Big Bang describes is not observed: 75% dark energy, 20% dark matter, 4% missing baryons. The rest, 1%, is fraught with “tensions” and therefore inconsistent. The Big Bang model explains nothing.
@RedshiftDrift
I know, that’s why I used the term “apparent”. What I meant is that the fact that astronomers detect something that looks like a relation between the CMB temperature and redshift doesn’t necessarily mean that this relation actually exists in physical reality. It could easily be an optical effect, an illusion or something arising from the way the observations are interpreted. Sorry, I didn’t explain myself very well.
@RedshiftDrift the paper is about modified electromagnetism SU(2) cartan modes instead of SU(1) There are 70+ occurrences of SU(2) in the paper, hard to miss. Most importantly you missed that this paper does not cancel temperature evolution it halves it (factor 1 become 0.6 but still 1+z) Hence in this paper at Z=15 the cmb temp is 27.5K instead of 43.6k.
@RedshiftDrift
I have to reluctantly (very reluctantly) agree with @LifeIsStrange. As the abstract of the paper itself makes clear, the authors are not disputing the existence of a redshift-dependent evolution of the CMB temperature. They’re simply proposing an alternative way of measuring that evolution and arguing that, by using their method, the evolution comes out to be roughly half of what’s obtained using standard methods. So the paper isn’t arguing that the evolution doesn’t exist (which is what would really be required in order to support a static interpretation); it’s simply arguing that the CMB temperature evolution may be significantly smaller than the value inferred through conventional measurements.
So far, the only author who has seriously tried to address the problem of CMB temperature evolution within the framework of a static universe is M.A. Cody: https://www.preprints.org/manuscript/202510.1525
The problem is that the model he proposes is still fundamentally evolutionary in nature. It describes a universe that began in a hot, dense state and eventually settled into a static configuration. So the universe in his model is static now, but it hasn’t been static eternally, which means it ultimately isn’t the kind of truly eternal static universe we’re looking for.
I never said the paper is arguing that the evolution doesn’t exist, what I retain from it is: “We point out that a modified temperature–redshift relation (T-z relation) of the cosmic microwave background (CMB) cannot be deduced by any observational method that appeals to an a priori thermalisation to the CMB temperature T of the excited states in a probe environment of independently determined redshift z.” (my highlight)
The SU(2) stuff is irrelevant to this discussion! What it says is that there is no accurate way to measure that temperature without using an a-priori estimate of that temperature as an input to the analysis.
I argue here https://github.com/orgs/a-cosmology-group/discussions/178#discussioncomment-7435822 that CMB temperature measurements use the expected answer to analyze data.
Here are three examples of papers where they ‘cheat’ by calculating what the CMB temperature should be and using it as an input to their analysis:
[52] Noterdaeme, P., Petitjean, P., Srianand, R., Ledoux, C., López, S.: The evolution of the cosmic microwave background temperature - Measurements of TCM B at high redshift from carbon monoxide excitation. A&A 526, 7 (2011) https://doi.org/10.1051/0004-6361/201016140
[53] Klimenko, V.V., Ivanchik, A.V.: The measurements of the CMB temperature in diffuse interstellar medium of the Milky-Way and high redshift galaxies based on excitation of CI fine-structure and H2 rotational levels. J. Phys.: Conf. Ser. 1697(1), 012013 (2020) https://doi.org/10.1088/1742-6596/1697/1/012013
[54] Riechers, D.A., Weiss, A., Walter, F., Carilli, C.L., Cox, P., Decarli, R., Neri, R.: Microwave background temperature at a redshift of 6.34 from H2O absorption. Nature 602, 7895 (2022) https://doi.org/10.1038/s41586-021-04294-5
@RedshiftDrift
I read the discussion you linked and, while going through it, I found a link to another discussion dealing with many of the same topics, so I ended up reading that one too. After reading both discussions, I think I finally understand your position much better and I get what you were trying to say. What you’re saying actually makes perfect sense!
I hope your upcoming paper on the CMB will address the topic of the temperature evolution. Having your ideas on this subject gathered together in a single paper would make things much more convenient for readers, since they wouldn’t have to dig through a bunch of different discussions and scattered forum posts just to piece your views together. 😂
Anyway, thanks for linking that discussion, it was genuinely helpful!
@luisenrique-arch thanks for the support. Temperature measurements of the CMB are very complex and varied. The discussions you read only cover one type of measurement that relies on atomic energy levels and galaxy models of the local radiation that excites these levels. The entire topic is too vast to be discussed in a single paper, and it would take me too much time to learn all these different techniques in order to be able to debunk papers, also a very time-consuming process.
Rather than trying to find fault in a large number of papers, my approach is to explain by which process the CMB is produced. (Indeed the discussions are scattered all over this forum :smile: and not easy to find.) Since the CMB is produced the same way anywhere in space, its temperature is the same everywhere. My upcoming paper gives only a preliminary description of the CMB calculation, the formal calculation will have to be done in the relativistic regime (which I have not done yet).
You can see the progress of my ideas by reading my earlier papers/posters chronologically (here, there are not that many) but publishing each tiny step takes a lot of time (I submitted the upcoming paper 5 months ago, answered all questions from both reviewers and updated the paper, but they are not returning any review requests and now the editor has started another search for more reviewers…) I understand their reaction: giving reviewers a method to calculate the temperature of the CMB from first principles shatters their belief in the Big Bang model, something hard to let go of because their careers depend on it.
@RedshiftDrift writes : >(Indeed the discussions are scattered all over this forum 😄 and not easy to find.)
Oh well, time for an unfortunate Master in Business Administration to come in ;-)
ACG threads with the name CMB in it:
Hobby horses of ACG individuals (-:
CMB in other ACG discussions:
@RedshiftDrift
As discussed previously, I totally understand your reluctance to accept that the CMB temperature increases at higher redshift distances, as I was in that position until a few years ago. I also tried to prove that there was an error in the analyses of the type you mention. I could not find one, at least for the technique you discuss here involving fine absorption lines in distant gas clouds. It is possible that an extra heating source of clouds could be through the Hubble luminosity of those clouds, but then again that effect should not scale with distance. I came to accept the mainstream position on this not because I could fully endorse those highly sophisticated measurements, but because the CMB temperature relationship could be explained in my shell universe model. The mainstream scientists - while totally befuddled on the Big Bang and now in denial with the Webb observations - are still scientists. They are actually trying to get at the truth in their tortured fashion. We should keep it in mind that at least some of their findings are valid.
Supposing that the CMB findings are valid - and that the supernova time dilation is also true - then there are actually three things that could be tied together: the Hubble redshift, the CMB temperature scale and supernova time dilation. The latter two each have a (1 + z) relation with the redshift. My point is that if you should happen to find the ‘correct’ redshift mechanism, then you will also have found the explanation for SN time dilation and CMB temperature scaling as well. Why settle for hitting a single, when you could be standing on third base with a triple?
It was suggested that selection effects could produce the apparent increase in temperature (perhaps by E. Lerner? H. Traunmuller? Or T. Eastman?) Brighter galaxies are easier to detect at greater distances, and since brighter means hotter, the CMB temperature appears to increase because atomic populations are more excited in those hot galaxies. There is also a problem in interpreting the SZ effect if all the CMB is assumed to come from behind every object we see. This interpretation changes the calculated temperature and has a dependence on z. (Probably suggested by E. Lerner.)
Of course they are valid in the LCDM framework, but there is no z dependence of the CMB temperature in a static cosmology (as Lakatos explained years ago :wink:)
I already have found the ‘correct’ redshift mechanism, it predicts the observed $d = c \ln(1+z)/H_0$ law, explains a SNe light curve ‘stretch’ that agrees with the (1 + z) relation, passes the Tolman test for non-expansion, predicts the value of the Hubble constant from the electron density in the IGM, describes the CMB as the same everywhere (with a temperature I am in the process of calculating from first principles), has an acceleration constant that happens to equal $2\pi$ times the MOND acceleration (i.e. MOND is not fundamental), predicts the Macquart relation, explains the galaxy-quasar associations discovered by Arp, etc… all that based on a single input: the measured intergalactic electron density; and without any free parameter. I already have more than two home runs with this!
@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
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:
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.
@RedshiftDrift
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.
@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!
@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.
@RedshiftDrift . Meanwhile I have
publishedanother 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).
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.