New Theory for Dark Matter and Dark Energy

Discussion:

 This part is dedicated to a chronological discussion of important  results, observations, and comments. 


23.05. 2025:
My comment on new Results of the “Dark Energy Spectroscopic Instrument, DESI”,
March/April 2025:

Key publications are:

a) DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints, DESI collaboration: arXiv:2503.14738v2 [astro-ph.CO] 26 Mar 2025
b) Extended Dark Energy analysis using DESI DR2 BAO measurements, DESI collaboration: arXiv:2503.14743v2 [astro-ph.CO] 3 Apr 2025

DESI has accumulated an enormous quantity of data over a period of 3 years. Maps of 18.7 million astronomical objects have been created to date, with an accuracy that allows very profound statements about the parameterization of our cosmos. În above publications this was done with the help of the signatures of baryonic oscillations (BAO). The trajectory a=a(t) described in my slide set (page 179) can be reconstructed from the observables “large-scale-distribution, BAO” and the “redshift z”. With much better clarity than earlier measurements, DESI shows a cosmos that can in no way do without a cosmological term Λ, or a „Dark Energy (DM)“.
Figure 1 in (a) shows the trajectory of the ΛCDM standard model as a rough overview. This means that the Hubble-constant reconstructed in this way is about 0.68, the density Ωm is about 0.3 and the curvature term is zero. The measurement accuracy of DESI is so high that slight fissures become recognizable in the measured trajectory a=a(t). Something is not right. The problem, of course, is that we don't really know anything about either "Dark Energy (DE)" or "Dark Matter (DM)" at the moment. So the “consensus” is obviously that DM must be set as a Newton-Boltzmann- ensemble in a CDM-picture (CDM: Cold Dark Matter). Therefore, any deviation from the standard must be assigned to DE, and the first Friedmann-Equation must be sufficient for a rough description of expansion history. The deviation, which was uncovered with the DESI, now consists in the result that, on closer analysis, the energy density of the “dark energy” obviously has a temporal variation. A two-parameter fit for the DE with an equation of state w=P/ρc2=w(w0,wa) is presented in the above-mentioned publications (a, b). This model is then called w0waCDM. Even such a two-parameter fit with modified equations of state leads to anomalies. For example, a best fit shows a violation of the so called "Null-condition" for large structures with ρc2 + P ≥ 0. 

Despite everything, it is thanks to the accuracy of the DESI measurement that a deeper insight into the nature of our cosmos is possible.

So I would like to dare to present my concerns about a “w0waCDM world” here. I can only do this because I am aware of the power of my theory. From the point of view of the new theory, the following in above publications in particular need to be discussed:

In the new theory, the interpretation of DM as an ensemble of individual particles, which can be described with Boltzmann or Newton in a CDM-picture, is not correct. Not even MOND can be explained in this way. I would even go so far as to say that any approach to DM that cannot explain MOND must be wrong. A Newton-Boltzmann ensemble for Dark Matter is completely unsuitable for explaining MOND as a phenomenon, as I have shown in the book and in the set of slides. 

Then the following applies to the DESI interpretations: The BAO scale is only considered as a calibration parameter for determining the scale factor a(t) in a flat Friedmann universe, if the DM also behaves like an ensemble of “cold particles”, as „CDM“. This is explicitly emphasized in publication (a) and is also expressed there in the exclusive use of the first Friedmann equation (equations 6-8 in (a), page 5). In the model of a condensation of “quantum dark matter (QDM)” or a quantized MOND coupling, the BAO scale would lose its status as a standard measure. This for the following reasons:

  • After the CMB, BAO no longer exists
  • The global ratio of baryons to DM changes after the CMB decoupling of matter and radiation.
  • Due to the mass matrix, DM prefers to condense where baryons are also present.
  • So, structures (clusters) of the CMB that have formed through BAO are frozen and even further fixed by additional DM.
  • Therefore, the BAO pattern in the distribution of matter for small z should remain almost identical in both peak positions and amplitudes. 
  • However, under the “fingerprint” of the baryon/dark matter ratio originating from the CMB, this proportion is changing.  
  • According to theory, there has been an increase in dark matter of about 20% from the state of the CMB-decoupling to the present day.


If our theory is correct, it follows that the frozen sound horizon can no longer be an invariant and thus no longer a calibration quantity. The scale factor a(t) or the Hubble constant now determines the relative size of the (frozen) sound horizon in comoving coordinates as f(z) and not vice versa. A degeneracy, as I demanded in slides (slide 179), no longer seems to be necessary either
The age of the oldest stars (13.5 billion years) and the measurement of the local Hubble constant remain as anchor values. Of course, the baryon/DM ratio for the CMB stage or the local mass fraction Ωm are also important.
How the observable structural units gain mass as additional DM in the course of light traveling from the CMB to us is part of the world model to be determined. First and foremost, this should not be a problem for DE, but rather a question for dark matter (DM). As can be seen from the slides, for "DM-condensation", there is no problem with the “Null-condition”. It is always fulfilled.
To summarize briefly: The theory favors the image of a "Λ-quantum dark matter (ΛQDM)" rather than a w0waCDM world, as described in the above publications from the DESI collaboration. Using our theoretical value for the cosmological constant Λ and a relative matter density of Ωm=0.315, we indeed obtain a value of h=0.735 for the local Hubble constant.
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25.04.2025: 

Article "Accelerated Structure Formation: The Early Emergence of Massive Galaxies and Clusters of Galaxies",
by Stacy S. McGaugh , James M. Schombert, Federico Lelli , and Jay Franck;
The Astrophysical Journal, 976:13 (19pp), 2024 November 20,
https://iopscience.iop.org/article/10.3847/1538-4357/ad834d 

Abstract: 

Galaxies in the early Universe appear to have grown too big too fast, assembling into massive, monolithic objects more rapidly than anticipated in the hierarchical Lambda cold dark matter (ΛCDM) structure formation paradigm. The available photometric data are consistent with there being a population of massive galaxies that form early (z > 10) and quench rapidly over a short (1 Gyr) timescale, consistent with the traditional picture for the
evolution of giant elliptical galaxies. Similarly, kinematic observations as a function of redshift show that massive spirals and their scaling relations were in place at early times. Explaining the early emergence of massive galaxies requires either an extremely efficient conversion of baryons into stars at z > 10 or a more rapid assembly of baryons than anticipated in ΛCDM. The latter possibility was explicitly predicted in advance by modified
Newtonian dynamics (MOND). We discuss some further predictions of MOND, such as the early emergence of clusters of galaxies and early reionization.

My comment:
Obviously, MOND alone results in very fast galaxy formation for z>10. According to the article, the genesis of galaxies with MOND can be approximated with a “monolithic” formation of structure. This is in contrast to the so-called “hierarchical structure formation”.

In fact, in slide 196 I briefly addressed such a “monolithic genesis”, only in different words. Here, rapid galaxy formation was necessary to more closely constrain the “Hubble discrepancy” within the allowed error range. So, if MOND suggests fast galaxy formation, then MOND as a phenomenon could be another building block for solving the Hubble-discrepancy. 

But why should MOND be a “cause” when I can explain MOND itself? No, the real reason for rapid galaxy formation lies in the duality of the mass matrix in the theory, with which MOND proves to be a pure phenomenon. This as a result of a general quantization for dark matter, where the a0 of MOND turns out to be intrinsic to galaxies, but not general. Specifically: We have to explain a possible quantum jump of DM from the CMB to galaxies!

I therefore assess the rapid galaxy formation described in the article as follows:

  • by using the parameter a0, MOND uses an implicitly higher proportion of DM than the hierarchical ΛCDM model. According to my theory, DM/m0=6.4 for MOND instead of DM/m0=5.44 for ΛCDM with the CMB simulation. Or: MOND implicitly has about twice the baryon mass (as DM) available as ΛCDM! Whereby MOND cannot explain the phase transition for global N=3 to N=2.
  • As shown in the article (eq. 6 here), the fast galaxy formation is due to the MOND potential, which goes proportional with ln(r). The hierarchical picture, including dark matter, uses an 1/r potential, i.e. an asymptotically flat potential. The higher mass of DM  could be of course an opportunity for the hierarchical model. With more mass (as DM) than for the CMB. But I don't see much chance for that either: without MOND as an expression of a “bosonic” ln(r) dependence for a potential, it won't work.
  • So: One question remains: Is there any phase change of DM from N=3 to N=2 in very short time? I have revealed: Such a phase jump for DM could be important for a solution of the Hubble discrepancy. So, what is reason for this transition? 

       

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03.03.2025

Comment on

J. Oppenheim, “A postquantum theory of classical gravity?” Phys. Rev. X 13, 041040 (2023).

J. Oppenheim recently presented a new approach that aims to unite quantum theory (QT) with classical gravitational theory (GRT) by leaving both worlds, i.e., QT and GRT, untouched. The consequence would be that there would be no quantization of spacetime and thus no quantization of gravity. In order to avoid the contradictions that usually arise in such “hybrid theories” (e.g., violation of the uncertainty principle for local objects such as electrons), Oppenheim must attribute a probabilistic element (“noise”) to spacetime, which is related to the classical motion of many particles (ensemble) in phase space. There is no further explanation for the origin of this noise. It is simply an assumption (1). An essential point is that the two systems do not mix/interfere with each other, but are, in a sense, complementary to each other.

In this context, experiments have also been proposed that, without measuring the gravitational field, could answer the question of whether gravity itself is a quantum field (2). The above-mentioned theory would then be one way of formulating a hybrid theory without contradictions.

Anyone who has studied my theory, or at least read the summary or even looked through the slides, should immediately recognize a certain semantic similarity with Oppenheim's theory. It is the incompatibility of both worlds, which I postulate as a law of nature in my theory. The world of QT, described by the variable “a,” and the world of GRT, described by the variable “b.” At a meta-level, my theory linked these two systems with a superordinate uncertainty relation. This ultimately allowed Mach's principle to be translated into a quantum mechanical calculation.  The classical element of phase space is that of “distant mass,” ideally described classically in terms of variable b.

One constraint of Oppenheim's theory for the GRT component is the timelike nature of the phase space described in it (v< c), ultimately a near field effect. From the standpoint of my theory, it makes sense to interpret the Oppenheim approach as described “in symmetry.” That is, with the scale length r0=R0=λ for both “a” and “b.” I have referred to this state in the text as “after delocalization.” If everything is correct, then, based on the consistency of a hybrid theory, one could now exploit the full potential that results from a symmetry breaking with Mach’s principle.

However, I am skeptical about the possible application of Oppenheim's theory to cosmological problems. In particular, I am suspicious of an explanation for modified Newtonian dynamics (MOND) published in (3). A critical analysis of (3) is provided in (4). The basis for the application to MOND is a fourth-order differential for a potential in a vacuum, namely ∇4Φ=0. After twofold integration in spherical symmetry, the most general solution is ∇2Φ=-C1/r + C2 with C1,2 as arbitrary constants. Since Φ is supposed to be a potential, -C1/r + C2 must be a (mass) density, even though a vacuum was actually assumed. If one is now tolerant and does not immediately set C1,2 equal to zero, Oppenheim et al. set the constant C1 as decisive for MOND and the constant C2 as related to the cosmological constant.  While an interpretation of the C2 term as cosmological constant is certainly possible, the C1 term has nothing at all to do with MOND.


If we now set ∇2Φ as Poisson differential for the above density, we obtain in spherical symmetry

Φ=-C1r/2 + C2r2/6 -C3/r +C4

For local masses, C2 and C4 can be set to zero, then

Φ=-C1r/2 -C3/r 

If C3 is interpreted as the Newtonian component, then according to Oppenheim, the linear component should cause MOND as a phenomenon. Interestingly, such type of potential is well known as the so called “Cornell-potential” for quark-confinement (5).

However, the potential required for MOND should be logarithmic:

ΦMOND~ln(r)


Only for such potential the Milgrom correlation and the empirical Tully-Fisher relation could be explained.

Nevertheless, the above result of Oppenheim's theory can possibly be interpreted as follows: Every type of “quantum matter” (baryonic matter nm0) must be assigned an additional density component, which should correspond to the stochastic character of spacetime. One would only have to change the metric, but not introduce something like a “graviton.” In a spherical geometry, a baryonic mass nm0 is then surrounded by another field, which acts like an additional mass “M”. However, this mass term would then have to be included in the GRT field equations as a “static field effect”. In other words: a breach of the principle of equivalence.
Now, it seems that the equivalence principle wants to tell us more than just the resulting GRT. So, we should admit a mutual correlation for two dynamically acting entities, but under no circumstances a violation of the equivalence principle. Our theory solves this problem by introducing a probability with the help of the “mass matrix” (slides, page 34).

In spherical symmetry, a metric of the form

-g00= 1+2Gnm0/r + 2GM(r)/r

is the result of Oppenheims approach, without the cosmological term. Such a metric is also provided by the “mass matrix” in our theory. This is after “delocalization” and with the correct behaviour for MOND!

The common feature here is a correlation between two types of matter: “quantum matter” which in my theory is called ‘baryonic’ with a Θ=-1, and the deterministic correlate, which in my theory is called “2M” with Θ=+1. In contrast to Oppenheim's theory, in my theory the correlation of the two types is a “can” but not a “must” condition. In conclusion, a kind of probability. Furthermore, the image of a “condensation of dark matter 2M” yields such accurate results that it could even explain the so-called “Hubble discrepancy”. This in combination with my theoretical value for the cosmological constant, which turns out as a pure combination of natural constants.

In my opinion, Oppenheim's theory is a promising approach and could be seen as a kind of confirmation of my general theory. The conflict between Oppenheim's theory and astronomical observations obviously lies in the fact that this approach does not consider the actual meta-level. In other words, the interdependence of both worlds, i.e., the local microscopic chaos and the orbits and years of the cosmos, which are formulated as “Mach's principle” and formalized in my theory as the complementarity of the world as such.


(1) Thomas Galley, „Might There Be No Quantum Gravity After All?“ Physics 16, 203, 2023 DOI: 10.1103/Physics.16.203
(2) S. Bose et al., „Spin Entanglement Witness for Quantum Gravity“, Phys. Rev. Lett. 119, 240401 – Published 13 December, 2017
(3) J. Oppenheim, A. Russo, „Anomalous contribution to galactic rotation curves due to stochastic spacetime“, arXiv:2402.19459v3 [gr-qc] 22 Jul 2024
(4) M. P. Hertzberg, A. Loeb „Critical Analysis of Replacing Dark Matter and Dark Energy with a Model of Stochastic Spacetime“, arXiv:2404.13037v6 [gr-qc] 20 Sep 2024
(5) Bali, G. S. "QCD forces and heavy quark bound states". Phys. Rep. 343 (1): 1–136. arXiv:hep-ph/0001312