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The impact of a fast decaying component of mass-energy, that decreases faster than radiation with the increase of the scale factor, on the evolution of the universe is studied using a hydrodynamic approach. Proceeding from the Hamiltonian formalism, the hydrodynamic-like equations for the velocity and acceleration of the expansion of the universe as a function of conformal time are obtained. The influence of a fast decaying component on the dynamics of the expansion of the universe is determined by the sign of its contribution to the total energy density of the system. The effects of this component are illustrated by figures., Comment: 6 pages, 2 figures

An analogy between non-relativistic quantum mechanics in the Madelung formulation and quantum geometrodynamics in the case of the maximally symmetric space is drawn. The equations equivalent to the continuity equation and the hydrodynamic Euler equation describing the evolution of the velocity introduced for the case of hypothetical fluid flow characterizing the cosmological system are obtained. It is shown that the perfect nature of the fluid is broken by the quantum Bohm potential. The quantum potential is calculated in semi-classical approximation for different forces acting in the system both in standard quantum mechanics and in minisuperspace model of quantum geometrodynamics. The explicit dependences of the cosmic scale factor on the conformal time, which take into account the quantum additive, are found for empty space with spatial curvature and for a spatially flat universe with dust and radiation., Comment: 17 pages, 3 figures

The Hubble tension is analyzed in the framework of quantum cosmological approach. It is found that there arises a new summand in the expression for the total energy density stipulated by the quantum Bohm potential. This additional energy density acts similarly to a stiff matter component, modifying the expansion history of the early universe and decaying with scale factor $a$ as $a^{-6}$, faster than radiation, in late universe. Taking account of this matter-energy component of quantum nature can, in principle, eliminate a discrepancy between the direct late time model-independent measurements of the Hubble constant and its indirect model dependent estimates. The considered model allows one to extend the standard cosmology to quantum sector., Comment: 14 pages, 1 figure, v.2: added a new section on numerical estimates, substantially updated the introduction and other sections, significantly expanded the list of references, revised the abstract, v.3: added a new section on stiff matter, expanded the list of references

Conditions under which a quantum particle is described using classical quantities are studied. The one-dimensional (1D) and three-dimensional (3D) problems are considered. It is shown that the sum of the contributions from all quantum corrections (in the WKB sense) strictly vanishes, when a quantum particle interacts with some specific medium. The indices of refraction of such media are found. In this case, the smallness of the Planck constant is not assumed. The momenta of quantum particles in these media and the wave functions of stationary states are determined. It is found that, for the 1D case, the wave function is similar to that of the test particle with zero binding energy in a singular attractive potential, which admits "fall" to the center. For the 3D case with central symmetry, a stationary state, describing a quantum particle with a classical momentum, is defined by the wave function, which has the resonance of width about two de Broglie wavelengths., Comment: 12 pages, 5 EPS figures, v.2: new formulas and figure are provided, discussion is extended, new references added, abstract is updated

A new derivation is given of the known generalized position-momentum uncertainty relation, which takes into account gravity. The problem of two massive particles, the relative motion of which is described by the Schroedinger equation, is considered. The potential energy is defined as a sum of `standard' non-gravitational term and the second one, which corresponds to gravitational attraction of particles as in Newton's theory of gravity. The Green's function method is applied to solve the Schroedinger equation. It is assumed that the solution of the problem in the case, when the gravitational interaction is turned off, is known. Gravity is taken into account in linear approximation with respect to the gravitational coupling constant made dimensionless. Dimensional coefficients at additional squares of mean-square deviations of position and momentum are written explicitly. The minimum length, determined as minimal admissible distance between two quantum particles, and the minimum momentum appear to be depending on the energy of particles' relative motion. The theory allows one to present the generalized position-momentum uncertainty relation in a new compact form., Comment: 12 pages, v.2: A comment on the Coulomb problem is added to Sect. 7

The new uncertainty relation is derived in the context of the canonical quantum theory with gravity for the case of the maximally symmetric space. This relation establishes a connection between fluctuations of the quantities which determine the intrinsic and extrinsic curvatures of the spacelike hypersurface in spacetime and introduces the uncertainty principle for quantum gravitational systems. The generalized time-energy uncertainty relation, which takes into account gravity, is proposed. It is shown that known Unruh's uncertainty relation follows, as a particular case, from the new uncertainty relation. As an example, the sizes of fluctuations of the scale factor and its conjugate momentum are calculated within an exactly solvable model. All known modifications of the uncertainty principle deduced previously from different approaches in the theory of gravity and string theory are obtained as particular cases of the proposed general expression., Comment: 13 pages, v.2: new section and title, abstract is revised

In the framework of the method of constraint system quantization, a quantum gravitational system (QGS) with the maximally symmetric geometry is studied. The state vector of the QGS satisfies the set of wave equations which describes the time evolution of a quantum system in the space of quantum fields. It is shown that this state vector can be normalized to unity. The generalization of the wave equations to the domain of negative values of the cosmic scale factor is made. For the arrow of time from past to future, the state vector describes the QGS contracting for the negative values of the scale factor and expanding for its positive values. The intensity distributions of matter are calculated for two exactly solvable models of spatially closed and flat QGSs formed by dust and radiation. The analogies with the motion in time of minimum wave packet for spatially closed QGS and with the phenomenon of diffraction in optics for flat QGS are drawn., Comment: 13 pages, 4 EPS figures

The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the Robertson-Walker metric. It is shown that the main equation of the quantum geometrodynamics is reduced to the non-linear Hamilton-Jacobi equation. Its non-linearity is caused by a new source of the gravitational field, which has a purely quantum dynamical nature, and is additional to ordinary matter sources. In the semiclassical approximation, the non-linear equation of motion is linearized and reduces to the Friedmann equation with the additional quantum source of gravity (or anti-gravity) in the form of the stiff Zel'dovich matter. The semiclassical wave functions of the universe, in which different types of matter-energies dominate, are obtained. As examples, the cases of the domination of radiation, barotropic fluid, or new quantum matter-energy are discussed. The probability of the transition from the quantum state, where radiation dominates into the state, in which barotropic fluid in the form of dust is dominant, is calculated. This probability has the same order of magnitude as the matter density contrast in the era of matter-radiation equality., Comment: 17 pages, v.2: Sect. 2 and 6 are revised, v.3: Sect. 2 is supplemented, new references are added

Quantum gravity may shed light on the prehistory of the universe. Quantum corrections to gravity affect the dynamics of the expansion of the universe. Their influence is studied on the example of the exactly solvable quantum model. The corrections to the energy density and pressure lead to the emergence of an additional attraction (like dark matter) or repulsion (like dark energy) in the quantum system of the gravitating matter and radiation. The model explains the accelerating expansion (inflation) in the early universe (the domain of comparatively small values of quantum numbers) and a later transition from the decelerating expansion to the accelerating expansion of the universe (the domain of the very large values of quantum numbers) from a single approach. The generation of primordial fluctuations of the energy density at the expense of the change of sign of the quantum correction to the pressure is discussed., Comment: 5 two-column pages, 4 EPS figures; v.2: refreshed and based on a talk given at the conference Fundamentals of Astroparticle and Quantum Physics, 17 - 23 September, 2017, BITP, Kyiv, Ukraine

The evolution of the universe is studied in exactly solvable dynamical quantum model with the Robertson-Walker metric. It is shown that the equation of motion which describes the expansion or contraction of the universe can be represented in the form of the law of conservation of zero total energy for a particle with arbitrary mass being an analogue of the universe. The analogue particle moves in the potential well under the action of the internal force produced by the curvature of space, matter, and pressures of classical and quantum gravitational sources. At a definite stage of the evolution of the universe, this force can perform the positive work on the universe, which is similar to the work of the repulsive forces of dark energy, or it does the negative work analogous to the work of the attractive forces of dark matter. The cases of real and complex state vectors which describe the geometrical properties of the universe filled with dust and radiation are considered. It is shown that predictions of the quantum model do not contradict the observational data about the accelerating expansion of our universe., Comment: 18 pages, 6 EPS figures; v.2: a few sections and abstract are revised, new references

The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schr\"{o}dinger equation complemented by the equations of motion for the momentum operator and its time derivative in Heisenberg's form reduce to the Einstein equations with an additional source of the gravitational field of quantum nature. The spatially closed universe with cosmological constant, originally filled with a uniform scalar field and radiation, is considered as quantum cosmological system. The perfect fluid in the form of radiation defines the material reference frame. The properties of the averaged scalar field which acts like ordinary matter are investigated. After averaging over its quantum states, the free scalar field turns into the Weyssenhoff fluid characterized by the energy density, pressure, and spin of constituent particles. The cases when the contribution of the quantum effects into the gravitational interaction becomes significant on macroscopic scale are analyzed. It is demonstrated that, unless the whole, at least a part of such matter-energy constituents as dark matter and dark energy may have a quantum origin., Comment: 20 pages, v.2: a few sections are revised, new references

The evolution of matter in the expanding FRW universe during the time interval between the end of inflation and the beginning of the radiation-dominated era is studied. A constraint between the global geometry and total amount of matter in the universe as a whole, which is valid during the phase of an intensive transfer of energy to the matter degrees of freedom, is introduced. The matter is considered as a perfect fluid with two components between which there is energy exchange. The analytical solutions of the Einstein equations are found. The limiting cases of the the Hubble expansion rate and the total energy density, which correspond to matter production, pressure-free and radiation-dominated phases are investigated. The transition to the inflationary phase and a unidirectional evolution of matter in the universe at all phases are discussed., Comment: 5 pages, talk given at the 5th Petrov International Symposium on High Energy Physics, Cosmology and Gravity (29 April - 05 May, 2012, Kiev, Ukraine)

We consider the cosmological model which allows to describe on equal footing the evolution of matter in the universe on the time interval from the inflation till the domination of dark energy. The matter is considered as a two-component perfect fluid imitated by homogeneous scalar fields between which there is energy exchange. Dark energy is represented by the cosmological constant, which is supposed invariable during the whole evolution of the universe. The matter changes its equation of state with time, so that the era of radiation domination in the early universe smoothly passes into the era of a pressureless gas, which then passes into the late-time epoch, when the matter is represented by a gas of low-velocity cosmic strings. The inflationary phase is described as an analytic continuation of the energy density in the very early universe into the region of small negative values of the parameter which characterizes typical time of energy transfer from one matter component to another. The Hubble expansion rate, energy density of the matter, energy density parameter, and deceleration parameter as functions of time are found., Comment: 10 pages, 2 EPS figures; v.2: new Section 5 (Conclusion), paragraphs about inflation and mechanical analogy are revised, references are added, some misprints are corrected

The standard cosmological model supposes that the dominant matter component changes in the course of the evolution of the universe. We study the homogeneous and isotropic universe with non-zero cosmological constant in the epoch when the dominant matter component has a form of a gas of low-velocity cosmic strings. It is shown that after the scale transformation of the time variable such a model and the standard model of a spatially flat universe filled with pressure-free matter provide the equivalent descriptions of cosmological parameters as functions of time at equal values of the cosmological constant. The exception is the behavior of the deceleration parameter in the early universe. Pressure-free matter can obtain the properties of a gas of low-velocity cosmic strings in the epoch when the global geometry and total amount of matter in the universe as a whole obey an additional constraint. This constraint follows from the quantum geometrodynamical approach in the semiclassical approximation. In terms of general relativity, its effective contribution to the field equations can be linked to the evolution in time of the equation of state of matter caused by the processes of redistribution of energy between matter components., Comment: 16 pages, 3 EPS figures, v.2: (i) model of a two-component perfect fluid with varying equation of state parameter is introduced to justify a complementary constraint between the global geometry and total amount of matter in the universe as a whole; (ii) paper is reorganized; (iii) abstract and section 5 are revised

It is shown that if one takes into account Mach's principle in the form which follows from quantum theory and considers it as a complementary constraint between the parameters which characterize the energy density and geometry of the universe in addition to Einstein equations for a FRW universe, non-relativistic matter transforms into an analogue of K-matter. The exact solutions of the Einstein equations for the universe with such matter and cosmological constant are found. It is demonstrated that the Machian universe under consideration with a nonzero cosmological constant is equivalent to the open de Sitter universe. In the limit of zero cosmological constant such a universe evolves as a Milne universe, but in contrast to it, it contains matter with nonzero energy density. The possible application of proposed approach to the description of the present cosmological data is discussed. The problem of the age of the universe is considered as an example., Comment: 9 pages, based on the talk given at International Conference on the Astroparticle Physics, Gravitation and Cosmology (7 - 10 June, 2011, Kiev, Ukraine)

In this paper we propose a model of production of ordinary and dark matter in the decay of a hypothetical antigravitating medium in the form of a condensate of (zero-momentum) spinless massive particles (denoted as $\phi$) which fills the universe. The decays of $\phi$-particles into baryons, leptons, and dark matter particles are caused by some (after-GUT) interaction with the mass scale between the electroweak and grand unification. The observed dark energy is identified with a portion of a condensate which has not decayed up to the instant of measurement. The decay rate of $\phi$-particles $\Gamma_{\phi}$ is expressed through the three parameters - the coupling constant $\alpha_{X}$, the mass scale $M_{X}$ which defines the mass of $X$-particle as the mediator of after-GUT interaction, and the energy imparted to the decay products. We show that the masses of dark matter particle $m_{\chi}\approx 5$ GeV and $\phi$-particle $m_{\phi}\approx 15$ GeV can be extracted from the 7-year WMAP and other astrophysical data about the contributions of baryon, dark matter, and dark energy densities to the total matter-energy density budget in our universe. Such a mass of light WIMP dark matter agrees with the recent observations of CoGeNT, DAMA, and CDMS. The obtained masses of $\phi$- and dark matter particle are concordant with the coupling constant of after-GUT interaction $\alpha_{X} \sim 1/70 at $M_{X} \sim 6 \times 10^{10}$ GeV, and the decay rate $\Gamma_{\phi} \approx 2 \times 10^{-18}\, {s}^{-1}$. The cross-sections of the reactions in which dark matter particles can be produced are calculated, Comment: 15 pages, 2 EPS figures, v.2: a few sections are revised, additional explanations and some corrections are provided

We give an estimation of the masses of light dark matter particle and dark energy quasiparticle which can be extracted from the astrophysical data about the contributions of baryon, dark matter, and dark energy densities to the total matter-energy density budget in our universe. We use the quantum cosmological model in which dark energy is a condensate of quantum oscillations of primordial scalar field. The dark energy quasiparticle with the mass ~ 15 GeV is consistent with the 7-year WMAP and other data. The quasiparticles can decay with violation of CP-invariance into baryons, leptons, and dark matter. The WIMP mass ~ 5 GeV corresponds to observed values of baryon and dark matter energy densities. Such a mass agrees with the observations of CoGeNT, DAMA, and CDMS. Quasiparticles of dark energy can be registered as a constant background of radiation with the frequency ~ 3.64 x 10^{24} 1/s. Dark matter particles must exhibit themselves in the form of signals with the frequency ~ 1.21 x 10^{24} 1/s of radiation from galaxy clusters where the intensive gravitational fields produced by dark matter exist., Comment: 9 pages, 1 EPS figure. v2: references added, remark about coincidence problem added, small grammatical corrections

The semi-classical approach to the quantum geometrodynamical model is used for the description of the properties of the universe on extremely small spacetime scales. Quantum theory for a homogeneous, isotropic and closed universe is constructed on the basis of a Hamiltonian formalism with the use of material reference system as a dynamical system defined by macroscopic relativistic matter. The equations of the model are reduced to the form of the Einstein-type equations in which the matter energy density has two components of quantum nature, which behave as antigravitating fluids. The first component does not vanish in the limit h -> 0 and can be associated with dark energy. The second component is described by extremely rigid equation of state and goes to zero after the transition to large spacetime scales. On small spacetime scales this quantum correction determines the geometry of the universe. This geometry is conformal to a unit four-sphere embedded in a five-dimensional Euclidean flat space. When reaching the post-Planck era, the geometry of the universe changes into the geometry conformal to a unit four-hyperboloid in a five-dimensional Lorentz-signatured flat space. Near the boundary between two regions the universe undergoes almost an exponential expansion which passes smoothly into the expansion under the action of radiation dominating over matter which is described by the standard cosmological model., Comment: 18 pages, 4 EPS figure

The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity effects ~ h exhibit themselves in the form of additional matter source with the negative pressure and the equation of state as for ultrastiff matter. The analytical solution of the equations of theory of gravity, in which matter is represented by the radiation and additional matter source of quantum nature, is found. It is shown that in the stage of the evolution of the universe, when quantum corrections ~ h dominate over the radiation, the geometry of the universe is described by the metric which is conformal to a metric of a unit four-sphere in a five-dimensional Euclidean flat space. In the radiation dominated era the metric is found to be conformal to a unit hyperboloid embedded in a five-dimensional Lorentz-signatured flat space. The origin of the universe can be interpreted as a quantum transition of the system from the region in a phase space with a trajectory in imaginary time into the region, where the equations of motion have the solution in real time. Near the boundary between two regions the universe undergoes almost an exponential expansion which passes smoothly into the expansion under the action of radiation dominating over matter. As a result of such a quantum transition the geometry of the universe changes. This agrees with the hypothesis about the possible change of geometry after the nucleation of expanding universe from `nothing'., Comment: 14 pages, 1 EPS figure

The origin of negative pressure fluid (the dark energy) is investigated in the quantum model of the homogeneous, isotropic and closed universe filled with a uniform scalar field and a perfect fluid which defines a reference frame. The equations of the model are reduced to the form which allows a direct comparison between them and the equations of the Einsteinian classical theory of gravity. It is shown that quantized scalar field has a form of a condensate which behaves as an antigravitating medium. The theory predicts an accelerating expansion of the universe even if the vacuum energy density vanishes. An antigravitating effect of a condensate has a purely quantum nature. It is shown that the universe with the parameters close to the Planck ones can go through the period of exponential expansion. The conditions under which in semi-classical approximation the universe looks effectively like spatially flat with negative deceleration parameter are determined. The reduction to the standard model of classical cosmology is discussed., Comment: 15 pages, v.2 additional explanations and a few corrections are provided

The exactly solvable quantum model of the homogeneous, isotropic and closed universe in the matter-energy production epoch is considered. It is assumed that the universe is originally filled with a uniform scalar field and a perfect fluid which defines a reference frame. The stationary state spectrum and the wave functions of the quantum universe are calculated. In this model the matter-energy in the universe has a component in the form of a condensate of massive zero-momentum excitation quanta of oscillations of primordial scalar field. The mean value of the scale factor of the universe in a given state is connected with the mass of a condensate by a linear relation. The nucleation rate of the universe from the initial cosmological singularity point is calculated. It is demonstrated that the process of nucleation of the universe can have an exponential (explosive) nature. The evolution of the universe is described as transitions with non-zero probabilities between the states of the universe with different masses of a condensate., Comment: 16 pages, v.2 a few misprints are corrected and small additional explanations are provided

It is shown that the homogeneous and isotropic Universe is spatially flat in the limit which takes into account the moments of infinitely large orders of probabilistic distribution of a scale factor with respect to its mean value in the state with large quantum numbers. The quantum mechanism of fine tuning of the total energy density in the Universe to the critical value at the early stage of its evolution is proposed and the reason of possible small difference between these densities during the subsequent expansion is indicated. A comparison of the predictions of the quantum model with the real Universe is given., Comment: 12 pages

It is shown that an accelerating expansion of the present-day Universe extracted from observed luminosity of the type Ia supernovae can be explained by quantum theory which takes into account feedback coupling between geometry and matter (like in Mach's principle). At the same time an accelerating expansion of the Universe is explained by the influence of small negative cosmological constant. A comparison with the model with positive cosmological constant (dark energy) which also has obtained its theoretical grounds in a structure of the developed formalism is made. Parameters of the Universe in the states with large quantum numbers are calculated., Comment: 12 pages, 1 EPS figure; to be published in Ukr. J. Phys

The quantum model of the homogeneous, isotropic, and spatially closed universe predicts an existence of two types of collective quantum states in the universe. The states of one type characterize a gravitational field, the others describe a matter (uniform scalar) field. In the first stage of the evolution of the universe a primordial scalar field evolves slowly into its vacuum-like state. In the second stage the scalar field oscillates about an equilibrium due to the quantum fluctuations. The universe is being filled with matter in the form of elementary quantum excitations of the vibrations of the scalar field. The separate quantum excitations are characterized by non-zero values of their energies (masses). Under the action of gravitational forces mainly these excitations decay into ordinary particles (baryons and leptons) and dark matter. The elementary quantum excitations of the vibrations of the scalar field which have not decayed up to now form dark energy. The numerical estimations lead to realistic values of both the matter density \Omega_{M} = 0.29 (with the contributions from dark matter, \Omega_{DM} = 0.25, and optically bright baryons, \Omega_{stars} = 0.0025) and the dark energy density \Omega_{X} = 0.71 if one takes that the mean energy ~ 10 GeV is released in decay of dark energy quantum and fixes baryonic component \Omega_{B} = 0.04 according to observational data. The energy (mass) of dark energy quantum is equal to ~ 17 GeV and the energy > 2 x 10^{10} GeV is needed in order to detect it. Dark matter particle has the mass ~ 6 GeV. The Jeans mass for dark matter which is considered as a gas of such massive particles is equal to M_{J} ~ 10^{5} M_{\odot}., Comment: 21 pages, 2 EPS figure; full version is submitted to the volume "Progress in Dark Matter Research" (Nova Science)

The quantum model of homogeneous and isotropic universe filled with the uniform scalar field is considered. This model predicts effective inverse square-law dependence of the mean total energy density <\rho> on the expectation value of cosmological scale factor where the averaging is performed over the state with large quantum numbers. Such a law of decreasing of <\rho> during the expansion of the universe allows to describe the observed coordinate distances to type Ia supernovae and radio galaxies in the redshift interval z = 0.01 - 1.8. A comparison with phenomenological models with the cosmological constant (\Lambda CDM) and with zero dark energy component (\Omega_{M} = 1) is made. It is shown that observed small deviations of the coordinate distances to some sources from the predictions of above mentioned simple quantum model can be explained by the fluctuations \delta a of the scale factor about the average value . These fluctuations can arise due to finite widths of quasistationary states in the early universe. During expansion the fluctuations \delta a grow with time and manifest themselves in the form of observed relative increase or decrease of coordinate distances. The amplitudes of fluctuations \delta a/ calculated from observed positions of individual supernovae are in good agreement with their estimations in quantum theory. Possible consequences from the conclusions of quantum theory are discussed., Comment: 17 pages, 3 EPS figure; full version is to appear in the volume "Progress in General Relativity and Quantum Cosmology Research" (Nova Science)

The quantum model of the homogeneous and isotropic universe predicts logarithmic-law dependence of coordinate distance to source on redshift z which is in good agreement with type Ia supernovae and radio galaxies observations for the redshift range z = 0.01 - 1.8. A comparison with phenomenological models with dark energy in the form of cosmological constant and without dark energy component is made. Fluctuations of the cosmological scale factor about its average value which can arise in the early universe produce accelerating or decelerating expansions of space subdomains containing separate sources with high redshift whereas the universe as a whole expands at a steady rate., Comment: 10 pages, 3 EPS figure, 1 table; remark on large-scale structure formation was added

On the basis of our quantum cosmological approach we show that there can be two previously unknown types of collective states in the universe. One of them relates to a gravitational field, another is connected with a matter (scalar) field which fills the universe on all stages of its evolution. The increase in number of the quanta of the collective excitations of the gravitational field manifests itself as an expansion of the universe. The collective excitations of the scalar field above its true vacuum reveal themselves mainly in the form of dark matter and energy. Under the action of the gravitational forces they decay and produce the non-baryonic dark matter, optically bright and dark baryons. We have calculated the corresponding energy densities which prove to be in good agreement with the data from the recent observations., Comment: 15 pages

In the present report we make an attempt to give an answer to the question of modern cosmology about the nature of the dark matter and energy in our universe. On the basis of our quantum cosmological approach, proposed in 1997-2002, we show that there can be two types of collective states in the universe. One of them relates to a gravitational field, another is connected with a matter (scalar) field which fills the universe on all stages of its evolution. The collective excitations of the scalar field above its true vacuum reveal themselves mainly in the form of dark matter and energy. Under the action of the gravitational forces they decay and produce the non-baryonic dark matter, optically bright and dark baryons. We have calculated the corresponding energy densities which prove to be in good agreement with the data from the recent observations., Comment: A talk given at the International Conference "Modern Problems of Theoretical Physics" Dedicated to the 90th anniversary of A.S. Davydov (December 9-15, 2002, Kiev, Ukraine); 8 pages (twocolumn)

Old and new puzzles of cosmology are reexamined from the point of view of quantum theory of the universe developed here. It is shown that in proposed approach the difficulties of the standard cosmology do not arise. The theory predicts the observed dimensions of nonhomogeneities of matter density and the amplitude of fluctuations of the cosmic background radiation temperature in the Universe and points to a new quantum mechanism of their origin. The large scale structure in the Universe is explained by the growth of nonhomogeneities which arise from primordial quantum fluctuations due to finite width of quasistationary states. The theory allows to obtain the value of the deceleration parameter which is in good agreement with the recent SNe Ia measurements. It explains the large value of entropy of the Universe and describes other parameters., Comment: to be published in Eur. Phys. J. C; 24 pages, 1 EPS figure, 1 table

Old and new puzzles of cosmology are reexamined from the point of view of quantum theory of the universe developed here. It is shown that in proposed approach the difficulties of the standard cosmology do not arise. The theory predicts the observed dimensions of the nonhomogeneities of matter density and the amplitude of the fluctuations of the cosmic background radiation temperature in the Universe and points to a new quantum mechanism of their origin. It allows to obtain the value of the deceleration parameter which is in good agreement with the recent SNe Ia measurements. The theory explains the large value of entropy of the Universe and describes other parameters., Comment: 21 pages, 1 EPS figure, 1 table; revised subsection 3.7

In a model of nonlinear system of three scalar fields the problem on dynamics of a massive particle moving in effective potential provided by two relativistic fields is solving. The potentials for these fields are chosen in the form of anti-Higgs and Higgs potentials. It is shown that the effective potential has the shape of two-hump barrier localized in spacetime. It tends to constant attractive potential at spacetime infinity. The magnitude of this constant constituent is determined by the Higgs condensate. It is shown that nonlinear equation of motion of a particle has the solutions which describe the capture of a particle by the barrier and the scattering on the barrier., Comment: 7 pages, 4 EPS figures

The idea of ``soft'' confinement when the lifetime of hadron with respect to quark-gluon channel of decay is greater or at least of the order of some characteristic time for our Universe is considered. Within the framework of a model of three nonlinearly interacting fields the explicit form of an effective potential is found. It provides the confinement of a massive particle within the limited region of space by means of constant component of the potential which arises as a result of reorganization of vacuum of one of the scalar fields. It is shown that the lifetime of hadron being equal to the age of the Universe leads to the Higgs boson with the mass m > 63.7 GeV and realistic self-constant., Comment: 6 pages, 2 EPS figures

Subject of this contribution is to demonstrate that the observed faintness of the supernovae at the high redshift can be considered as a manifestation of quantum effects at cosmological scales. We show that observed redshift distribution of coordinate distances to the type Ia supernovae can be explained by the local manifestations of quantum fluctuations of the cosmological scale factor about its average value. These fluctuations can arise in the early universe, grow with time, and produce observed accelerating or decelerating expansions of space subdomains containing separate supernovae with high redshift whereas the universe as a whole expands at a steady rate., Comment: 22 pages, 7 EPS figures; a contribution to the International workshop on Frontiers of Particle Astrophysics, Kiev, June 21 - 24, 2004

The classical and quantum models of the Friedmann universe originally filled with a scalar field and radiation have been studied. The radiation has been used to specify a reference frame that makes it possible to remove ambiguities in choosing the time coordinate. Solutions to the Einstein and Schroedinger equations have been studied under the assumption that the rate of scalar-field variation is much less than the rate of universe expansion (contraction). It has been shown that, under certain conditions, the quantum universe can be in quasistationary states. The probability that the universe goes over to states with large quantum numbers owing to the interaction of the scalar and gravitational fields is nonzero. It has been shown that, in the lowest state, the scale factor is on order of the Planck length. The matter- and radiation-energy densities in the Planck era have been computed. The possible scenarios of Universe evolution are discussed., Comment: 11 pages, 1 EPS figure

A highly excited Friedmann universe filled with a scalar field and radiation has been considered. On the basis of a direct solution to the quantum-mechanical problem with a well-defined time variable, it has been shown that such a universe can have features (energy density, scale factor, Hubble constant, density parameter, matter mass, equivalent number of baryons, age, dimensions of large-scale fluctuations, amplitude of fluctuations of cosmic microwave background radiation temperature) identical to those of the currently observed Universe., Comment: 9 pages