DM is among the most important open problems in both cosmology and particle physics. There are three prominent hypotheses on nonbaryonic DM, namely Hot Dark Matter (HDM), Warm Dark Matter (WDM), and Cold Dark Matter (CDM).

The lightest Neutralino with the rest energy (>300 GeV) is an excellent candidate to form the universe’s CDM [9] . The most widely discussed particles for nonbaryonic CDM are commonly assumed to be WIMPs. The Lee-Weinberg limit restricts their rest energy to >2 GeV [10] .

It is known that a Sterile Neutrino with rest energy in 1.6 ⟺ 10 keV range is a good WDM candidate [11] .

HDM is a theoretical form of DM which consists of particles that travel with ultra-relativistic velocities. An example of a HDM particle is a Neutrino [12] . In WUM, the particles of HDM are XIONs (see Section 3.2).

The prospect that DMPs might be observed in Centers of Macroobjects has drawn many new researchers to the field in the last forty six years. Indirect effects in cosmic rays and gamma-ray background from the annihilation of CDM in the form of heavy stable neutral leptons in Galaxies were considered in pioneer articles [13] - [18] .

The dark matter problem can be, in principle, achieved in the approach of extended gravity. This is stressed, for example, in the famous paper of Prof. C. Corda [19] .

Two-component DM system consisting of bosonic and fermionic components is proposed for the explanation of emission lines from the bulge of the Milky Way galaxy. C. Boehm, P. Fayet, and J. Silk analyze the possibility of two coannihilating neutral and stable DMPs: a heavy fermion for example, like the lightest neutralino (>100 GeV) and the other one a possibly light spin-0 particle (~100 MeV) [20] .

Multicomponent DM models consisting of both bosonic and fermionic components were analyzed in literature (for example, see [21] - [27] and references therein). An article by G. Bertone and T. M. P. Tait [28] provides an excellent review of what we have learned about the nature of DM from past experiments, and the implications for planned DM searches in the next decade.

It is the main goal of WUM to develop a Model based on two dimensionless parameters only: the dimensionless Rydberg constant α and the time-varying parameter Q, which is a measure of the Size and Age of the World. In WUM, we often use well-known physical parameters, keeping in mind that all of them can be expressed through the Basic Units. Taking the relative values of physical parameters in terms of the Basic Units we can express all dimensionless parameters of the World through two parameters α and Q in various rational exponents, as well as small integer numbers and π [29] .

In our view, there is no way to prevent an occurrence of the Initial Singularity in BBM. A Finite World must have gotten started in a principally different way—a Fluctuation in the Eternal Universe with an extrapolated finite size that equals to the basic size unit a [30] :

a = 1.7705641 × 10 − 14   m

The size of this Fluctuation can increase with a finite speed c (gravitodynamic constant). Then, there is no need to introduce Cosmological Inflation. However, a question about the mechanism of Continuous Creation of Matter in the World arises.

In 1952, Y. Nambu proposed an empirical mass spectrum of elementary particles with a mass unit close to one quarter of the mass of a pion ( m 0 / 2 ≅ 35   MeV / c 2 ) [31] . He noticed that meson masses are even multiplies of a mass unit m 0 / 2 , baryon (and also unstable lepton) masses are odd multiplies, and mass differences among similar particles are quantized by m 0 ≅ 70   MeV / c 2 . During many years M. H. Mac Gregor studied this property extensively [32] . In WUM, we introduce a Basic Energy Unit E₀ that equals to:

E 0 = h c / a = 70.025252   MeV

where h is the Planck constant. It is worth noting that the rest energy of electron E e equals to: E e = α E 0 and the Rydberg unit of energy is: R y = h c R ∞ = 0.5 α 3 E 0 = 13.605692   eV ( R ∞ is the Rydberg constant).

According to WUM, the Eternal Universe is the Creator of the World’s DM. Ordinary Matter (7.2%) is a byproduct of DMPs self-annihilation. It means that rest energies of DMPs must be constant and proportional to the basic energy unit E₀ [30] . Considering the main goal of WUM—two dimensionless parameters only—the rest energies of DMPs should be proportional to constant α only.

Following the mechanism discussed by C. Boehm, et al., we proposed multicomponent DM system consisting of two couples of co-annihilating DMPs: a heavy Dark Matter Fermion (DMF)—DMF1 (1.3 TeV) and a light spin-0 boson—DIRAC (70 MeV) that is a dipole of Dirac’s monopoles with charge μ = e / 2 α (e is the elementary charge); a heavy fermion—DMF2 (9.6 GeV) and a light spin-0 boson—ELOP (340 keV) that is a dipole of preons with electrical charge e/3; DMF3 (3.7 keV), DMF4 (0.2 eV), and boson XION (10.6 μeV).

In frames of WUM, Dark Matter Particles DMF1, DMF2, and DMF3 have rest energies, which corresponds to rest energies of Neutralinos, WIMPs, and Sterile Neutrinos discussed in literature (see Section 3.1). DMF4 constitute the biggest shell of DM Cores of Superclusters [33] .

DIRAC, which is a magnetic dipole of Dirac’s monopoles, is introduced to explain the Dirac’s quantization condition. The quantum theory of magnetic charge started with a paper by P. Dirac in 1931 [34] . In this paper, he showed that if any magnetic monopoles exist in the universe, then all electric charge in the universe must be quantized. The electric charge is, in fact, quantized, which is consistent with (but does not prove) the existence of monopoles. Since Dirac’s paper, several systematic monopole searches have been performed but it remains an open question whether monopoles exist [35] . In our opinion, all electric charges are quantized due to existence of DIRACs—dipoles of Dirac’s monopole, which are the smallest building blocks of the structure of constituent quarks and hadrons (mesons and baryons).

ELOP, which is an electric dipole of preons with the rest energy ( E e / 3 = 170.333   keV ), is introduced to explain all subatomic particles with electrical charge ∝ e / 3 . Preons are the smallest building blocks of the structure of quarks and leptons. According to I. A. D’Souza and C. S. Kalman “In particle physics, preons are postulated ‘point-like’ particles, conceived to be subcomponents of quarks and leptons” [36] .

S. Sukhoruchkin has this to say about “A Role of Hadronic effects in Particle Masses” [37] : We discuss relations in particle mass spectrum and consider results of analysis of spacing distributions in nuclear spectra which show a distinguished character of intervals related to the electron mass and nucleon mass splitting. Systematic appearance of stable nuclear intervals rationally connected with particle mass splitting 170-340-510-1020 keV… was found in levels of different nuclei including low-spin levels observed in (γ, γ) and (n, γ) reactions. In this work we show such tuning effect in numerous levels from new compilation for light nuclei. Together with long-range correlations in nuclear binding energies they provide a support for the observed correlation between masses of hadrons and leptons (including masses of nucleons and m_e).

We did not consider binding energies of DIRACs and ELOPs, and thus the values of their rest energies are approximate. They have negligible electrostatic and electromagnetic charges because the separation between charges is very small. They do however possess electrostatic and electromagnetic dipole momentum [38] .

XION, which is introduced in the present paper for the first time, is an analog of Axion discussed in literature (see Introduction). It has the value of the rest energy 10.6 μeV that is in reasonable agreement with the value of ≳5 μeV discussed in [7] and with highly-motivated mass range between 5 ⟺ 11 μeV discussed in [39] . In our view, XIONs are responsible for the Le Sage’s mechanism of gravitation [30] .

The reason for this multicomponent DM system was to explain:

· The diversity of Very High Energy gamma-ray sources in the World [40] ;

· The diversity of DM Cores of Macroobjects of the World (Superclusters, Galaxies, and Extrasolar Systems (ESS)), which are Fermion Compact Objects and DM Reactors in WUM [30] .

WUM postulates that rest energies of DMFs and bosons are proportional to the basic energy unit E₀ multiplied by different exponents of α and can be expressed with the following formulae:

DMF1 (fermion): E D M F 1 = α − 2 E 0 = 1.3149948   TeV

DMF2 (fermion): E D M F 2 = α − 1 E 0 = 9.5959804   GeV

DIRAC (boson): E D I R A C = α 0 E 0 = 70.025252   MeV

ELOP (boson): E E L O P = 2 / 3 α 1 E 0 = 340.66596   keV

DMF3 (fermion): E D M F 3 = α 2 E 0 = 3.7289394   keV

DMF4 (fermion): E D M F 4 = α 4 E 0 = 0.19857107   eV

XION (boson) E X I O N = α 6 E 0 = 10.574179   μ eV

We still do not have a direct confirmation of DMPs’ rest energies, but we do have a number of indirect observations. The signatures of DMPs self-annihilation with expected rest energies of 1.3 TeV; 9.6 GeV; 70 MeV; 340 keV; 3.7 keV are found in spectra of the diffuse gamma-ray background and the emissions of various Macroobjects in the World [39] . We connect observed gamma-ray spectra with the structure of Macroobjects (nuclei and shells composition). Self-annihilation of those DMPs can give rise to any combination of gamma-ray lines. Thus, the diversity of Very High Energy gamma-ray sources in the World has a clear explanation.

In this regard, it is worth recalling a story about neutrinos: “The neutrino was postulated first by W. Pauli in 1930 to explain how beta decay could conserve energy, momentum, and angular momentum (spin). But we still don’t know the values of neutrino masses”. Although we still cannot measure neutrinos’ masses directly, no one doubts their existence.

Neutrons serve as another example. The mass of a neutron cannot be directly determined by mass spectrometry since it has no electric charge. But since the masses of a proton and of a deuteron can be measured with a mass spectrometer, the mass of a neutron can be deduced by subtracting proton mass from deuteron mass, with the difference being the mass of the neutron plus the binding energy of deuterium.

DMPs do not possess an electric charge. Their masses cannot be directly measured by mass spectrometry. Hence, they can be observed only indirectly due to their self-annihilation and irradiation of gamma-quants.

According to A. G. Oreshko, “P. L. Kapitsa supposed that a ball lightning is a window in another world”. We analyzed the possibility of the existence of other Worlds: Micro-World, Small-World, and Large-World based on the proposed Weak, Super-Weak and Extremely-Weak interaction respectively. It was suggested that Ball Lightning is an object of the Small-World. Below we discuss main characteristics of the proposed new Worlds in the Multiworld.

Macro-World. According to WUM, strength of gravity is characterized by gravitational parameter G [42] :

G = G 0 × Q − 1

where G 0 = a 2 c 4 8 π h c is an extrapolated value of G at the Beginning of the World ( Q = 1 ). Q in the present Epoch equals to: Q = 0.759972 × 10 40 . The range of gravity equals to the size of the World R:

R = a × Q = 1.34558 × 10 26   m

The total mass of the Macro-World M t o t is:

M t o t = 6 π 2 m 0 × Q 2 = 4.26943 × 10 53   kg

where m 0 is a basic mass unit: m 0 = h / a c , and average density ρ M W :

ρ M W = 3 ρ 0 × Q − 1 = 8.87794 × 10 − 27 kg / m 3

that equals to the critical density.

WUM foresees three additional types of interactions: Weak, Super-Weak, and Extremely-Weak, characterized by the following parameters respectively:

G W = G O × Q − 1 / 4

G S W = G O × Q − 1 / 2

G E W = G O × Q − 3 / 4

In our view, each type of interaction provides integrity of the corresponding World (see Table 1).

Large-World is characterized by a parameter G E W , which is about 10 orders of magnitude greater than G. The range of the extremely-weak interaction R E W in the present epoch equals to:

R E W = a × Q 3 / 4 = 1.44115 × 10 16   m = 1.5233   ly = 96335   AU

In our view, ESS are Large-World objects with spherical boundary between ESS and Intergalactic Medium. This boundary has a surface energy density σ 0 = h c a 3 . Maximum total mass of ESS equals to:

M E W = M E S S = 4 π σ 0 R E W 2 c 2 = 4 π m 0 × Q 3 / 2 = 1.03928 × 10 33   kg = 522.645 M ⊙

and maximum mass of Star M S t a r that is one third of M E S S :

M S t a r = 3.46427 × 10 32   kg = 174.215 M ⊙

Average density ρ E W equals to:

ρ E W = 3 ρ 0 × Q − 3 / 4 = 8.28918 × 10 − 17 kg / m 3

which is about 10 orders of magnitude greater than the critical density. Extremely-weak interaction between DM Cores and all particles around them provide integrity of ESS.

Small-World is characterized by the parameter G S W , which is about 20 orders of magnitude greater than G. The range of the super-weak interaction R S W in the present epoch equals to:

R S W = a × Q 1 / 2 = 1.54351 × 10 6   m

A maximum total mass of Small-World M S W is:

M S W = 4 π m 0 × Q = 1.19215 × 10 13   kg

and average density ρ S W equals to:

ρ S W = 3 ρ 0 × Q − 1 / 2 = 7.73947 × 10 − 7 kg / m 3

which is about 20 orders of magnitude greater than the critical density. According to WUM, Ball Lightning is an object of the Small-World.

Micro-World is characterized by the parameter G W , which is about 30 orders of magnitude greater than G. The range of the weak interaction R W in the present epoch equals to:

R W = a × Q 1 / 4 = 1.65314 × 10 − 4   m

that is much greater than the range of the weak nuclear force (10⁻¹⁶ ⟺ 10⁻¹⁷ m). The introduced principally new Weak Interaction between DMPs provide integrity of all Macroobjects’ Cores, which are 3D fluid balls, made up of different fermions, with a very high viscosity and act as solid-state objects. In our view, weak interaction between particles DMF3 provides integrity of DM Fermi Bubbles [30] .

With Nikola Tesla’s principle at heart—There is no energy in matter other than that received from the environment—we apply to the Micro-World the following equation for a maximum total mass M W :

M W = 4 π σ 0 R W 2 c 2 = 4 π m 0 × Q 1 / 2 = 1.36752 × 10 − 7   kg = 6.28331 M P l

where M P l is the Planck mass. The average density of the Micro-World ρ W is:

ρ W = 3 ρ 0 × Q − 1 / 4 = 7.22621 × 10 3 kg / m 3

In our opinion, Micro-World objects with mass about Planck mass (we name them PLANCKs) are the smallest building blocks of all Macroobjects.

In WUM, the time-varying Gravitational parameter G ∝ τ − 1 is proportional to the energy density of the Medium ρ M ∝ τ − 1 . It is not constant. That is why WUM aligns gravity with the Le Sage’s kinetic theory of gravitation, which proposes a mechanical explanation for Newton’s gravitational force in terms of streams of tiny unseen particles impacting all material objects from all directions. According to this model, any two material bodies partially shield each other from the impinging corpuscles, resulting in a net imbalance in the pressure exerted by the impact of corpuscles on the bodies, tending to drive the bodies together [43] .

In WUM, Gravitation is a result of simple interactions of XIONs with Matter which work cooperatively to create a more complex interaction. XIONs are responsible for the Le Sage’s mechanism of gravitation [8] . This theory defines Gravity as an emergent phenomenon. Gravity is not an interaction but a manifestation of the Medium.

The validity of this statement follows from the work of L. Spitzer [44] and A. M. Ignatov [45] who identified Le Sage’s mechanism as a significant factor in the behavior of dust particles and dusty plasma.

We emphasize that DMPs do not interact via gravity. Two particles or microobjects will not exert gravity on one another when both of their masses are smaller than the Planck mass. Planck mass can then be viewed as the mass of the smallest macroobject capable of generating the gravitomagnetic field and serves as a natural borderline between classical and quantum physics. Incidentally, in his “Interpreting the Planck mass” article [46] , B. Hammel showed that the Plank mass is a lower bound on the regime of validity of General Relativity.

According to Le Sage theory, Gravitation is a “push” mechanism that depends on the screening effect of XIONs (10.6 μeV) by macroobjects with minimum Planck mass.

In WUM, XIONs have a high concentration in the World n X I O N (see Section 4):

n X I O N = 3.013034 × 10 14   m − 3

It means that a distance between XIONs a X I O N is:

a X I O N = 1.491645 × 10 − 5   m

which is much smaller than the range of the Weak interaction R W (see Section 3.3):

R W = a × Q 1 / 4 = 1.65314 × 10 − 4   m

Due to the Weak interaction, XIONs can collect into clouds with distances between particles smaller than R W . As a result, clumps of XIONs will arise. Larger clumps will attract smaller clumps and DMPs and initiate a process of expanding DM clumps up to the Planck mass, which can interact each other gravitationally.

On June 28, 2023, NANOGrav announced:

Astrophysicists using large radio telescopes to observe a collection of cosmic clocks in our Galaxy have found evidence for gravitational waves that oscillate with periods of years to decades, according to a set of papers published today in The Astrophysical Journal Letters. The gravitational-wave signal was observed in 15 years of data acquired by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) Physics Frontiers Center (PFC), a collaboration of more than 190 scientists from the US and Canada who use pulsars to search for gravitational waves. International collaborations using telescopes in Europe, India, Australia and China have independently reported similar results.

While earlier results from NANOGrav uncovered an enigmatic timing signal common to all the pulsars they observed, it was too faint to reveal its origin. The 15-year data release demonstrates that the signal is consistent with slowly undulating gravitational waves passing through our Galaxy.

“This is key evidence for gravitational waves at very low frequencies,” says Vanderbilt University’s Dr. Stephen Taylor, who co-led the search and is the current Chair of the collaboration. “After years of work, NANOGrav is opening an entirely new window on the gravitational-wave universe.”

Unlike the fleeting high-frequency gravitational waves seen by ground-based instruments like LIGO (the Laser Interferometer Gravitational-wave Observatory), this continuous low-frequency signal could be perceived only with a detector much larger than the Earth. To meet this need, astronomers turned our sector of the Milky Way Galaxy into a huge gravitational-wave antenna by making use of exotic stars called pulsars. NANOGrav’s 15-year effort collected data from 68 pulsars to form a type of detector called a pulsar timing array. Now, their 15 years of pulsar observations are showing the first evidence for the presence of gravitational waves, with periods of years to decades (15 years equal to 4.734 × 10⁸ s) [47] .

In the present paper, we discuss the proposed conjecture in detail. In our analysis, we use analogy between Electromagnetism and Gravitomagnetism. In WUM, the World consists of stable elementary particles with lifetimes longer than the age of the World. Protons with mass m p and electrons with mass m e have identical concentrations in the World: n p = n e . Intergalactic plasma (IGP) consisting of protons and electrons has plasma frequency ω p l :

ω p l 2 = 4 π n e e 2 4 π ε 0 m e = 4 π n e α h 2 π m e c c 2 = 2 n e a c 2

where ε 0 is the permittivity of free space. We emphasize that plasma frequency depends only on the concentration of particles, which constitute the plasma. By analogy between Electromagnetism and Gravitomagnetism, we define an ensemble of the objects with Planck mass (PLANCKs) in the Medium as “Gravitoplasma”, a maximum concentration of which can be calculated from Medium’s energy density ρ M :

ρ M = 2 ρ 0 × Q − 1 = M P l R S W 3 = 2 m 0 × Q 1 / 2 a 3 × Q 3 / 2 = n P l M P l

where n P l is a maximum concentration of Gravitoplasma:

n P l = R S W − 3 = 0.2720 × 10 − 18   m − 3

Then, an equation for Gravitoplasma frequency ω P l is:

ω P l 2 = 2 n P l a c 2 = 8.655 × 10 − 16   s − 2

ω P l = 2.942 × 10 − 8   s − 1

ν P l = 4.682 × 10 − 9   s − 1 = 4.682   nHz

In our view, the Super-weak interaction between PLANCKs with distance between them equals to R S W provides integrity of Gravitoplasma. Cosmic Gravitational Background is produced by Gravitational interaction between oscillating PLANCKs. Gravitational waves with frequency are smaller than ν P l cannot propagate in Gravitoplasma. It is worth noting that the calculated value of ν P l is the maximum value of Gravitoplasma frequency in case when the Medium consists of PLANCKs only. The calculated value of ν P l is in good agreement with the results obtained in [47] .

When a distance between PLANCKs is larger than R S W , then the integrity of Gravitoplasma provides the Extremely-weak interaction between them. In this case, Gravitoplasma frequency is lower than the calculated value ν P l . Gravitoplasma can be viewed as a cloud of “cosmic dust particles” with the size up to R E W = 1.44115 × 10 16   m = 1.5233   ly .

PLANCKs can also be responsible for the cosmic Far-Infrared Background, which is part of the Cosmic Infrared Background, with wavelengths near 100 microns that is the peak power wavelength of the black body radiation at temperature 29 K [48] .