抖阴APP导航 physicists propose theory of new cosmic phase transition
Scientific group working on the probl械m of evolution of Aether-axion configurations, left ro right: Dr. V. A. Popov, student K.R. Valiullin, Prof. A.B. Balakin, Dr. A.F. Shakirzyanov, PhD student G. D. Kiselev, Dr. D.E. Groshev, Dr. T.Yu. Alpin
抖阴APP导航 physicists have presented an axionic extension of the Aetheric version of the Einstein-Dirac theory in a paper The main element of this article is a spinor modification of the kinetic term attributed to the pseudoscalar field, which was implemented through the introduction of an effective metric. This modification allows one to describe the backreaction of the spinor field on the cosmic axionic dark matter.
The paper analyzes cosmological applications of the extended theory. The authors address the problem of the cosmic phase transition that occurred at the junction of two eras: the inflationary era and the subsequent era of matter domination. In the scientific literature, this transition is associated with the production of a significant number of massive particles that stopped the inflation.
“The graphs of the evolution of the Universe radius clearly show an inflection point, near which the cosmic phase transition and the associated change of eras occurred. Around the same time, the relic electromagnetic radiation emerged,” explains Alexander Balakin, Professor of the Department of General Relativity and Gravitation of the Institute of Physics.
From a physical perspective, this transition is accompanied by the creation of a colossal number of massive and massless particles. These include heavy fermions (quarks, protons, neutrons, and their antiparticles), light fermions (electrons, positrons), and massless neutrinos. In the language of quantum field theory, all these particles are described by spinor fields. The process of a catastrophic growth of the fermion number in the early Universe is known as “spontaneous spinorization.”
At the same time, there was a sharp increase in the number of bosons and pseudobosons, among which axions are particularly significant. In subsequent epochs of the Universe expansion, relic axions formed the principal fraction of the cosmic dark matter, and fermions became the building blocks of astrophysical objects.
The central element of the proposed extension of the theory is the so-called effective metric. Its construction includes a four-vector of the Aether velocity and a kernel, which depends on spinor invariants.
“The first ‘effective metric’ in the history of physics was proposed by the German physicist Walter Gordon in 1923. If we add the product of the components of the velocity of the medium, through which a photon travels, to the metric of physical spacetime, multiplying it by a kernel containing the refraction index of this medium, we obtain an optical metric, which contains information about the dielectric and magnetic properties of this moving medium. The dynamics of photons propagating in a real transparent medium, moving non-uniformly and non-linearly, is equivalent to the motion of photons along a geodesic line in a fictitious space with the resulting optical metric,” says the interviewee.
In the presented work, the Gordon’s idea is applied to the axion dynamics. The velocity is the velocity of the dynamic Aether, and the kernel is a function depending on the fermion number density.
“Thus, we took into account the backreaction effect of the spinor field on the axion field, with the dynamic Aether acting as a kind of ‘moderator’ in this interaction model,” the scientist notes.
In previous studies, spinor modifications were introduced into the Aether Lagrangian. In the new version, they were transferred to the kinetic term of the axion field.
“Over the past 10 years, we have constructed a full-format ‘control theory’ for the behavior of axion systems, which is mediated by the dynamic Aether field through a guiding function introduced into the axion field potential. Two years ago, my student, Amir Shakirzyanov, successfully defended his dissertation on this topic. We then expanded this idea by introducing a control function into the axion field potential that depends on spinor invariants. Then with my student Anna Efremova we introduced the spinor control function into the kinetic term of the axion field Lagrangian, introducing this control function as the kernel of the effective metric. Thus, the problem of control in the Aetheric-axionic cosmic field configuration has been completely resolved,” comments Dr Balakin.
Since the kernel of the effective metric contains a spinor field, encoded in one scalar and one pseudoscalar invariants, the paper obtained a modification of the effective mass matrix and a corresponding complication of the evolution equations for the spinor quantities. Similar modifications have been encountered in the works of other authors, but in those cases they were included in the Lagrangian of the spinor field itself and were not formally related to the axion field. In the presented version, the effective mass of the spinor field contains a term proportional to the square of the derivative of the axion field.
“Two concepts are used for the description of fermions: first, the intrinsic rest mass of a free particle, second, the effective mass due to an external force acting on the particle. If a fermion called a neutrino has zero intrinsic rest mass but exposed to the influence of the external force, it is ‘slowed down’ by this force and moves as if it actually had this mass. This is the so-called axionically induced effective mass of the fermion,” the researcher explains. The problem of neutrino mass is widely discussed in theoretical and experimental contexts and is known as “neutrino oscillations.”
One interesting detail emerges, when the expansion scalar of the Aetheric flow takes some specific value.
“In the plasma electrodynamics, the charge shielding effect is well known. There is an electric charge carrier, but the electric field around it disappears as soon as you move beyond the boundary of the sphere of the Debye radius. Here, the situation is similar: axions are present, but their gravitational field is, in a sense, ‘shielded’ due to interactions with the Aether,” the professor adds. The control function, which enters the total Lagrangian through the axion field potential, plays a key role. In canonical axion field theory, this function is treated as a constant, ensuring the invariance of the Lagrangian under discrete transformations of the axion field. In the presented model, the control function depends on the coordinates through the expansion scalar of the Aether flow. Under discrete transformations of the axion field, the potential component remains unchanged, but the gradient of the control function is no longer zero. The authors showed that the extended Lagrangian of the axion field is invariant under discrete transformations, if the control function satisfies a certain key equation.
“We have proven that the key equation for the evolution of the control function is not simply an ansatz, but a mathematically rigorous consequence of the invariance of the complete Lagrangian under discrete transformations of the axion field,” emphasizes Alexander Balakin.
The scientists note the backreaction effect of spinor field evolution on cosmodynamics. In one of the solutions obtained, the number of fermions first increases, reaches the maximum and then decreases.
“We can state that we have presented a mathematically consistent model, according to which namely the dynamic Aether first initiates and then terminates the process of intense particle production. During the active production phase, the number of particles produced grows anomalously. After this process ceases, the growth stops, and during the expansion process, the density decreases, as their total number is distributed throughout the increasing volume of the Universe,” elaborates the scientist.
Answering the question, why do many researchers try to find exact solutions obtained for substantially simplified models, the expert states, “Solutions presented as integrals and even graphical illustrations don’t fully convince readers, but if the results are presented in the form of well-known analytical functions, any skeptic is forced to agree”.
Speaking about further testing of the developed theory, Dr. Balakin notes that he himself is a theoretician, but sees possible avenues for verifying the model, “Since 1997, I have been actively developing non-minimal field theory, the essence of which is to describe the interaction of electromagnetic, gauge, vector, scalar, axion, and spinor fields with spacetime curvature. This story culminated in a paper published in late 2025 in the journal Symmetry. It was shown that the interaction of a spinor field with curvature can trigger 鈥榮pontaneous spinorization鈥� in the early Universe. But at the early stages of the Universe evolution, when the spacetime curvature is large enough, its effect can be reflected in the initial matter density distribution. The imprint of this distribution is visible in the map of temperature fluctuations in the cosmic microwave background radiation, based on data from the Planck space observatory. I would prioritize this task.”