arXiv subjects

V. V. Kuzmichev

Publications and source records attributed to V. V. Kuzmichev.

At least 19 recordsLinked to original sources

arXiv2026

On primordial matter production induced by spatial curvature in the early universe

In this note, it is shown that nonvanishing spatial curvature produces primordial matter in the initially empty universe due to quantum gravity effects. This matter decays faster than radiation and is described by a stiff equation of state. The quantum Hamiltonian constraint equation for the universe with the maximally symmetric geometry is solved in the semi-classical approximation. The extra energy density and pressure of quantum origin that appear in the generalized Friedmann equations describe primordial matter and modify the expansion history of the early universe.

gr-qc↗

arXiv2025

Scalar fields with power-law potentials in quantum cosmology

A homogeneous and isotropic quantum cosmological system (universe) initially filled with a uniform scalar field that has a potential in the power law representation is considered. Depending on the epoch, this scalar field yields barotropic matter in the form of stiff matter, perfect gas, radiation, dust, cosmic strings, domain walls, de Sitter vacuum, or phantom matter. The proposed approach is based on quantum geometrodynamics for the maximally symmetric space. The relevant differential equations for the separate power-law summands of the scalar field potential and the corresponding quantum Hamiltonian constraint equations, which describe the universe that can be viewed as dominated by one form or another of barotropic matter, were obtained. The solutions to these equations have been found in analytical form.

gr-qc↗

arXiv2024

Cosmology with the matter component decaying faster than radiation

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.

gr-qc↗

arXiv2024

Minisuperspace model of quantum geometrodynamics in the Madelung-Bohm formalism

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.

gr-qc↗

arXiv2024

The Hubble tension from the standpoint of quantum cosmology

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.

gr-qc↗

arXiv2020

On the conditions for the classicality of a quantum particle

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.

quant-ph↗

arXiv2020

Uncertainty principle in quantum mechanics with Newton's gravity

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.

quant-ph↗

arXiv2018

Generalized uncertainty principle in quantum cosmology for the maximally symmetric space

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.

gr-qc↗

arXiv2017

Quantum dynamics of the early universe

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.

gr-qc↗

arXiv2016

The matter-energy intensity distribution in a quantum gravitational system

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.

gr-qc↗

arXiv2015

Comparative description of the evolving universe in classical and quantum geometrodynamics

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.

gr-qc↗

arXiv2014

Quantum geometrodynamical description of the dark sector of the matter-energy content of the universe

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.

gr-qc↗

arXiv2013

Quantum corrections to the dynamics of the expanding universe

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 Schrödinger 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.

gr-qc↗

arXiv2012

Cosmological consequences of the redistribution of energy between matter components in the very early universe

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.

gr-qc↗

arXiv2012

Two-component perfect fluid in FRW universe

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.

gr-qc↗

arXiv2012

Low-velocity cosmic strings in accelerating universe

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.

astro-ph.CO↗

arXiv2011

K-matter as Mach's principle realization

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.

astro-ph.CO↗

arXiv2011

Production of matter in the universe via after-GUT interaction

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 $ϕ$) which fills the universe. The decays of $ϕ$-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 $ϕ$-particles $Γ_ϕ$ is expressed through the three parameters - the coupling constant $α_{X}$, 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 $m_χ\approx 5$ GeV and $ϕ$-particle $m_ϕ\approx 15$ 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 $ϕ$- and dark matter particle are concordant with the coupling constant of after-GUT interaction $α_{X} \sim 1/70 at $M_{X} \sim 6 \times 10^{10}$ GeV, and the decay rate $Γ_ϕ \approx 2 \times 10^{-18}\, {s}^{-1}$. The cross-sections of the reactions in which dark matter particles can be produced are calculated

hep-ph↗