We propose conformal invariance as a fundamental symmetry governing cosmological particle creation from vacuum fluctuations, employing a phenomenological approach with an ideal fluid action to address the long-standing back-reaction problem. Within the framework of our model, we argue that particle production cannot in general emerge from classical vacua but suggest it must originate from a quantum vacuum at zero scale factor , subject to the assumptions of discrete particle number, induced gravity, and a specific choice of the source function Phi. We further suggest that the transition surface is consistent with being a null boundary in a limiting sense rather than space-like. This suggests that particles are created on the light cone and may remain causally connected, with their apparent simultaneity being potentially illusory. Our model is consistent with an open Universe ( k=0,-1) and offers a possible reinterpretation of the Big Bang as a detonation wave propagating through quantum vacuum at the speed of light.

A complete mathematical model of the generation of radiation and electromagnetic effects inside crystalline dielectrics and at their surface has been constructed. The case of exposure to powerful flows of soft X-ray radiation is considered. The mathematical model is based on the photon and electron transport equations, kinetic equations for photoelectrons, and semi-classical kinetic equations for secondary charge carriers. The system of equations is closed by self-consistent Maxwell equations. The transport equations consider in detail the processes of the electron-photon cascade. For secondary charge carriers, conduction electrons, and valence band holes, the processes of scattering by phonons are taken into account. A comparison of the results obtained using simpler models with the results of applying the complete mathematical model is provided.

Short review of the Weyl geometry is given. To describe the phenomenological particle creation we suggest the modified perfect fluid model taking into account the back reaction on the geometry of both the already created particles and the very process of their creation. It is found that the relation for particle creation is conformal invariant. This requires the creation law consisting of the source terms as the Weyl Lagrangian plus two quite new terms depending of the particle number density.

The action of an ideal fluid in Euler variables with a variable number of particles is used for the phenomenological description of the processes of particle creation in strong external fields. It has been demonstrated that the conformal invariance of the creation law imposes quite strict restrictions on the possible types of sources. It is shown that combinations with the particle number density in the creation law can be interpreted as dark matter within the framework of this model.

On the sapphire R-plane, ultrathin Mo films with a thickness of less than 10 nm, which are resistant to oxidation for a long time, were grown. For these films, the appearance of the Stranski-Krastanow type islands was first observed in the thickness range of 1-1.6 nm after the growth process was interrupted. The base diameter of islands and their height were similar to 100-150 nm and 20-25 nm, respectively. At maximum thickness values in this range (1.6 nm), the island formation was not fully completed, and each large island consisted of a set of smaller ones. In the rest of the thickness range, only the substrate relief was observed in the atomic force microscope (AFM) images, which is typical for two-dimensional film growth.

Using the example of an action for an ideal fluid with a variable number of particles, we study a phenomenological description of the processes of particle production in the background of strong external fields, including gravity and scalar fields. This model is discussed for Weyl geometry and Riemannian geometry. A new invariant related to the interaction of the Weyl vector with particles is incorporated into the considered matter action. The conformal invariance of the term in the matter action responsible for the particle production is demonstrated.

We investigated the possibility of the homogeneous and isotropic cosmological solution in Weyl geometry, which differs from the Riemannian geometry by adding the so called Weyl vector. The Weyl gravity is obtained by constructing the gravitational Lagrangian both to be quadratic in curvatures and conformal invariant. It is found that such solution may exist provided there exists the direct interaction between the Weyl vector and the matter fields. Assuming the matter Lagrangian is that of the perfect fluid, we found how such an interaction can be implemented. Due to the existence of quadratic curvature terms and the direct interaction the perfect fluid particles may be created straight from the vacuum, and we found the expression for the rate of their production which appeared to be conformal invariant. In the case of creating the Universe 'from nothing' in the vacuum state, we investigated the problem, whether this vacuum may persist or not. It is shown that the vacuum may persist with respect to producing the non-dust matter (with positive pressure), but cannot resist to producing the dust particles. These particles, being non-interactive, may be considered as the candidates for dark matter.

Iron island films were grown on sapphire by pulsed laser deposition with in situ electrical resistance control, which made it possible to precisely determine the percolation transition. Four growth stages can be distin-guished: initial nucleation, independent island growth, ripening with channel formation, and island coalescence into a labyrinth structure. The morphology of the iron island films corresponded to these stages, depending on the time and deposition rate at a given temperature. At growth temperatures of T >= 350 degrees C, the percolation thickness exponentially depended on the temperature. The electrical response time t of the system to a single pulse was<1 s, and the temperature dependence of 1/t was linear in Arrhenius coordinates with a slope cor-responding to an activation energy of 0.41 eV. The dependence of the film thickness and island diameter on the pulse frequency before the onset of the percolation transition reached a maximum, which can be explained by two competing factors: diffusion stimulation owing to the high kinetic energy of the incident particles and an increase in the number of initial nuclei in the substrate regions without islands.

A short introduction to Weyl geometry and Weyl gravity is given. The self-consistency relation for the variation of the general form of the matter action integral to be conformal invariant is obtained. It is shown that the particle production rate per unit coordinate volume per unit coordinate time is conformal invariant. It is noticed that such a feature allows us to consider the perfect fluid action as an example of the Sakharov™s induced gravity model.

Using a model for an ideal fluid with a variable number of particles, a phenomenological description of the processes of particle production in strong external fields is investigated. The conformal invariance of the creation law is shown, which imposes rather rigorous restrictions on the possible types of sources. It appears that the combinations with the particle number density can imitate dark matter within this model.

These are lectures for students at the summer school conducted by the Faculty of Fundamental Sciences, Bauman Moscow State Technical University at 2022.

The gas-dynamic parameters of an ionized medium formed during impact ionization of a rarefied gas by fast electrons are considered. The concentration, drift velocity, and specific energy of low-energy secondary electrons are constructed by an approximate solution of the kinetic equation. Approximations of the spatial homogeneity of the kinetic equation and the isotropy of the initial distribution of secondary electrons during impact ionization are used. Additional approximations are related to the structure of the distribution function of secondary electrons and averaging of the cross sections.

Using the principle of least action, the motion equations for a singular hypersurface of arbitrary type in quadratic gravity are derived. Equations containing the "external pressure" and the "external flow" components of the surface energy-momentum tensor together with the Lichnerowicz conditions serve to find the hypersurface itself, while the remaining ones define arbitrary functions that arise due to the implicit presence of the delta function derivative. It turns out that neither double layers nor thin shells exist for the quadratic Gauss-Bonnet term. It is shown that there is no "external pressure" for null singular hypersurfaces. The Lichnerowicz conditions imply the continuity of the scalar curvature in the case of spherically symmetric null singular hypersurfaces. These hypersurfaces must be thin shells if the Lichnerowicz conditions are necessary. It is shown that for this particular case the Lichnerowicz conditions can be completely removed therefore a spherically symmetric null double layer exists. Spherically symmetric null singular hypersurfaces in conformal gravity are explored as application.

Co2FeAl (CFA) films with uniaxial magnetic anisotropy are obtained in ultrahigh vacuum using pulsed-laser evaporation on the A-plane of sapphire with a 10-nm seed layer of tungsten (110) epitaxially grown at a temperature of 450°C. The orientation of the crystallographic axes in the grown films is the same as for the growth of Fe (110) films on the same substrate. For some films, an inverse dependence of the anisotropic magnetoresistance is found, which may indicate implementation of the half-metal state. For other films from the same series, the inverse dependence is not observed since random factors, such as distortions of the lattice parameters, stresses in it, and various structural defects, can lead to loss of the half-metal properties.

Scanning tunneling microscopy and atomic force microscopy were used to study the topography of epitaxial Mo films of small thicknesses grown on the R-plane of sapphire. The domain of parameters of the Kardar–Parisi–Zhang model for the evolution of film surface profile in which it corresponds to the experimental results is found.

The homogeneous and isotropic cosmological model in the Weyl conformal geometry is considered. We showed that, despite the conformal invariance, the dust matter is allowed in such a universe. It is shown that the number of dust particles is not conserved, i.e. they are continuously produced. The general form of the law for their creation is found.

Arrays of magnetic nanocontacts are fabricated by growing Fe island films and filling the space between the islands with antiferromagnetic layers. The magnetic structures of the islands and their dependences on their dimensions are studied using atomic-force microscopy and micromagnetic calculations. Micromagnetic numerical calculations of the influence of the spin-polarized current flowing from the ferromagnetic edge into the antiferromagnetic interlayer on magnetization in magnetic antiferromagnet sublattices are carried out. The magnetization skew angle in magnetic antiferromagnet sublattices is found as a function of the current density.

In this thesis, we attempt to gain a more complete insight into Double Layer Theories in Weyl Gravity. In order to do this, we first establish the premise of Weyls Theory, including its provenance, development and flaws. This is all discussed in the first five chapters of the thesis. After having established Weyls Infinitesimal geometry and his gauged (scalar-tensor) gravity theory, we move onto the topic at hand, namely, Double Layers. We define the action to be used and describe the volume of integration (especially the Singular Hyper Surface) across which the action principle is setup. We define our gauss Normal Coordinate system and the scheme which we follow when we undertake our calculation. The following sections detail the variation process, in a succinct manner, taking turn by turn, each of the four parameters of our Quadratic Lagrangian. In the last chapter, we conclude the thesis by gleaning out the meaning behind our newfound surface energy tensor terms and what they might imply physically, as well as drawing a clearer picture of contrast between General Relativity and Weyl gravity.

In construction of the conformal invariant Lagrangian we restrict ourselves to the so-called Quadratic Gravity. Then, in the Riemannian geometry there exist only one suitable combination, namely, the square of the Weyl tensor (completely traceless part of the curvature tensor). The corresponding left-hand side of the field equations, the Bach tensor, is linear in the Weyl tensor itself and its second covariant derivatives. But, for any homogeneous and isotropic cosmological space-time (i.e., Robertson-Walker metric with arbitrary scale factor) the Weyl tensor is identically aero. Thus, any cosmological metric is the vacuum solution of the Weyl gravity in the framework of the Riemannian geometry – no matter at all! In 1919 Hermann Weyl invented a new geometry, which is now called the Weyl geometry. He introduced some 1-form and incorporated it into the connections by demanding that the new covariant derivative of the metric tensor coefficient equals this 1-form times that very coefficient. Then, he showed that in order these new connections to be conformal invariant, the 1-form must behave under the conformal transformation of the metric as the gauge field. It was the great discovery! How about the cosmology in the Weyl geometry? We started with construction the Lagrangian for the single particle moving in the given gravitational field in the Weyl geometry and discovered that there may exist some new interaction, absent in the Riemannian geometry (and, particularly, in General Relativity). This is due to the existence of the yet another invariant, namely, the contraction of the 1-form with the particle four-velocity vector. We called it “the invariant B”. And we were able to incorporate it into the Lagrangian for the perfect fluid. The cosmological principle requires that the Weyl 1-form should have only one (temporal) non-vanishing component depending only on the time coordinate. Hence, it can be removed by a suitable conformal transformation (also depending only on time). In such a gauge all possible functions of our new invariant B are converted into the set of some constants. The corresponding solutions we called “the basic solutions”. Given the basic solutions, the general ones are obtained by the arbitrary time-depending conformal transformation of both metric tensor and the 1-form. The important role in the existence of the non-trivial cosmological solutions is played by the possibility of the particle creation. The important problem is the comparison with the observations. By doing that and extracting some consequences we are using the cosmological equations of General Relativity, namely, the Friedmann equation. But now our gravitational equations are quite different. Therefore, we must rewrite them as the Friedman equations on the right-hand-side and some effective energy-momentum tensor on the left-hand-side. Of course, such an effective energy-momentum tensor may have nothing in common with the primary one. It appears that in the rather simple non-trivial basic solution we found, the effective energy-momentum tensor contains the cosmological term absent at the beginning. The details we will be presented in the talk.

We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of motion. There is the special gauge in choosing the conformal factor when the Weyl vector equals zero. In this gauge we found new vacuum cosmological solutions absent in General Relativity. Also, we found new solution in Weyl geometry for the radiation dominated universe with the cosmological term, corresponding to the constant curvature scalar in our special gauge. Possible relation of our results to the understanding both dark matter and dark energy is discussed.