卷 25, 编号 4 (2019)
- 年: 2019
- 文章: 15
- URL: https://journals.rcsi.science/0202-2893/issue/view/10822
Article
Wave Function of the Universe, Path Integrals and Gauge Invariance
摘要
—The paper is devoted to some of the difficulties which the Wheeler-DeWitt quantum geometrodynamics encountered, in particular, a strong mathematical proof that this theory is gauge-invariant, the definition of the wave function of the Universe through a path integral and the illegality of asymptotic boundary conditions in quantum gravity, the derivation of the Wheeler-DeWitt equation from the path integral and the equivalence of the Dirac quantization scheme with other approaches, the problem of definition of physical states in quantum gravity, possible realizations of the Everett concept of “relative states.” These problems are rarely discussed in the literature. They are related to the guiding idea that quantum theory of gravity must be gauge-invariant. It will lead to the question if it is possible to achieve this goal in a mathematically consistent way.
Matrix Wheeler-DeWitt Equation, Quantum Cosmological Tunneling and Three-Dimensional Space
摘要
To give a possible explanation of the 3-dimensionality of space, a matrix version of the Wheeler-DeWitt equation for quantum gravity is developed. In this equation, the number of spatial dimensions D is associated with a discrete variable. In this framework, a toy quantum-cosmological model for the birth of the universe from nothing is constructed. Here, nothing means a precosmic state with no classical space-time, but constituted by a collection of potential universes in different dimensions. The tunneling probability for the birth of a closed (D + 1)-dimensional Friedmann-Lemaitre-Robertson-Walker space-time is calculated, and two particular cases are distinguished: (1) In the interpretation of parallel universes, we find that there is no preferred number of spatial dimensions. Then, the 3-dimensionality of space is explained by the anthropic principle. (2) In the interpretation of a single universe, we find a solution showing that, under certain assumptions, a 3-dimensional space is preferred.
The Fractal Structure of Space Entails Origin of Pauli’s Equation
摘要
This study links the fractal structure of physical space-time to quantum-mechanical laws. It is shown that primitive distortions of the pregeometric surface, a fractal cell of 3D space, gives birth to a condition eliminating the metric defect while providing “eternal validity” of the exclusive algebras (of real, complex, and quaternion numbers). Written in the physical units typical for the micro-world entities, this condition acquires the precise form of the Pauli equation describing mechanics of the quantum electron with spin.
Dark Matter Particles: Properties and Detections
摘要
One of the most accepted ideas in modern cosmology to explain a number of puzzling astronomical observations is the existence of Dark Matter in the Universe, even though it has not been directly observed. We recall the motivation for its existence according to its influence on visible matter and its characteristics in terms of famous candidate particles.
Influence of the Gravitational Field of a Null String Domain on the Dynamics of a Test Null String
摘要
The paper studies the influence of periodically changing boundary conditions on the motion of a test null string “inside” an axially symmetric null string domain that has a layered structure and preserves its size. It is shown that the action of the gravitational field of the null string domain on a test null string whose size (radius) is smaller than the size of the domain, under any initial conditions, leads to oscillations of the test null string inside a limited spatial region. The motion (drift) of the region where the test null string oscillations take place, depends on the relationship between the initial parameters characterizing the test null string and the null string domain. These regions can be considered as particles with an effective nonzero rest mass, localized in space. It is noted that the properties of these particles should be determined by the trajectories of null strings moving within a limited spatial volume, and under the influence of changing external conditions, one sort of particles can pass into another one.
Spherically Symmetric Black Holes and Wormholes in Hybrid Metric-Palatini Gravity
摘要
The so-called hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. This paper gives a complete description of static, spherically symmetric vacuum solutions of HMPG in the simplest case where its scalar-tensor representation has a zero scalar field potential V(ϕ), and both Riemannian (R) and Palatini \((\mathcal{R})\) Ricci scalars are zero. Such a scalar-tensor theory coincides with general relativity with a phantom conformally coupled scalar field as a source of gravity. Generic asymptotically flat solutions either contain naked central singularities or describe traversable wormholes, and there is a special two-parameter family of globally regular black hole solutions with extremal horizons. In addition, there is a one-parameter family of solutions with an infinite number of extremal horizons between static regions and a spherical radius monotonically changing from region to region. It is argued that the obtained black hole and wormhole solutions are unstable under monopole perturbations. As a by-product, it is shown that a scalar-tensor theory with V(ϕ) = 0, in which there is at least one nontrivial (ϕ ≠ const) vacuum solution with R ≡ 0, necessarily reduces to a theory with a conformal scalar field (the latter may be usual or phantom).
What Can the Anthropic Principle Tell Us about the Future of the Dark Energy Universe
摘要
An anthropic explanation of the evident smallness of the dark energy (DE) density value implies the existence of a time-dependent component of the scalar field, serving, together with a negative-valued cosmological constant, as one of two components to the overall DE density. The observers (i.e. us) might then only evolve in those regions of the universe where the sum of those two components (the positive and a negative ones) is sufficiently close to zero. However, according to Vilenkin and Garriga, the scalar field component has to slowly but surely diminish in time. In about a trillion years, this process will put a cap to the now-observable accelerated expansion of the universe, leading to a subsequent phase of impending collapse. However, the vanishing scalar field might also produce some rather unexpected singularities with a finite nonzero scale factor. We analyze this possibility using a particular example of a Sudden Future Singularities (SFS) and come to a startling conclusion that the time required for an SFS to arise must be “comparable” to the lifetime of the observable universe.
Weak-Field Limit of a Kaluza-Klein Model with a Nonlinear Perfect Fluid
摘要
The main purpose of our paper is to construct a viable Kaluza-Klein model satisfying the observational constraints. To this end, we investigate a six-dimensional model with spherical compactification of the internal space. Background matter is considered in the form of a perfect fluid with nonlinear equations of state both in the external/our and internal spaces, and the model is set to include an additional bare cosmological constant Λ6. In the weak-field approximation, the background is perturbed by a pressureless gravitating mass that is a static pointlike particle. The nonlinearity of the equations of state of the perfect fluid makes it possible to solve simultaneously a number of problems. The requirement that the post-Newtonian parameter γ be equal to 1 in this configuration, first, ensures compatibility with the gravitational tests in the Solar system (deflection of light and time delay of radar echoes) at the same level of accuracy as General Relativity. Second, it translates into the absence of internal space variations, so that the gravitational potential exactly coincides with the Newtonian one, securing the absence of a fifth force. Third, the gravitating mass remains pressureless in the external space, as in the standard approach to nonrelativistic astrophysical objects and, meanwhile, acquires an effective tension in the internal space.
The Self-Consistent Field Method and the Macroscopic Universe Consisting of a Fluid and Black Holes
摘要
The article discusses and substantiates a self-consistent approach to the macroscopic description of systems with gravitational interaction. Corrections to the equation of state of the fluid are found, based on the macroscopic Einstein equations which were obtained by averaging over microscopic spherically symmetric metric fluctuations created by primordial black holes in a fluid medium. It is shown that these corrections are effectively equivalent to addition to the system of a fluid with the equation of state p = −ε. In addition, it is shown that, in this case, the mass of black holes can grow at a modern stage of evolution to very large values.
A Cosmological Scenario with Rotation
摘要
A Bianchi type IX cosmological model with expansion and rotation has been constructed in the framework of general relativity. The model comprises the Friedmannian stages of the Universe evolution including the subsequent transition to accelerated exponential expansion observed nowadays. The gravitational field sources of the model are ultrarelativistic matter, dust and a comoving anisotropic rotating dark energy. The possibility of detecting the cosmological rotation by astrophysical observations is discussed.
On the Description of Masses and Charges in the 6D Theory of Kaluza-Klein Type
摘要
We analyze two branches of five-dimensional theories from a methodological point of view: Kaluza’s theory and the Klein-Fock-Rumer (KFR) 5-optics, aimed at a geometric description of electromagnetism and masses of elementary particles, respectively. These two theories have a number of problematic points such as the Planckian masses in Kaluza’s theory, or appearing of a configuration space in the KFR scheme. We propose a simple six-dimensional toy model of Kaluza-Klein type with compactification on a two-dimensional torus \(\mathbb{T}^2\), which demonstrates a possible way to overcome these difficulties in quite a simple manner. The key features of our approach are: merging of the above two 5D theories into a unique 6D theory; using the signature (+-) of extra space allowing one to renormalize the mass spectrum; and a special kind of truncation of the full isometry group to the electromagnetic gauge group U(1). The latter feature allows a geometrical interpretation in terms of an effective 5D theory on a hypersurface \(\Sigma\subset\mathbb{T}^2\) being a leaf of a linear foliation of the 2-torus. Possible consequences and open questions arising in such a scheme are briefly discussed.
Dyon-Like Black Hole Solutions in the Model with Two Abelian Gauge Fields
摘要
Dilatonic black hole dyon-like solutions are overviewed in the gravitational 4D model with a scalar field, two 2-forms, two dilatonic coupling constants λi ≠ 0, i = 1, 2, obeying λ1 ≠ − λ2, and the sign parameter ε = ±1 before the scalar field kinetic term. Here ε = −1 corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions, when \(\lambda_i^2 \neq 1/2\) for ε = −1. Several integrable cases, corresponding to the Lie algebras A1 + A1, A2, B2 = C2 and G2 are considered. Some physical parameters of the solutions are derived: the gravitational mass, scalar charge, Hawking temperature, black hole area entropy and PPN parameters β and γ. Bounds on the gravitational mass and scalar charge, based on a certain conjecture, are presented.
Conservative Relativistic Algebrodynamics Induced on an Implicitly Defined World Line
摘要
In the framework of the Stueckelberg-Wheeler-Feynman concept of a “one-electron Universe” we consider a world line implicitly defined by a system of algebraic (precisely, polynomial) equations. A collection of pointlike “particles” of two kinds on the world line (or its complex extension) is defined by the real (complex conjugate) roots of the polynomial system and is detected then by an external inertial observer through light cone connections. Then the observed collective dynamics of the particle ensemble is, generally, subject to a number of Lorentz-invariant conservation laws. Remarkably, this property follows from the Vieta formulas for roots of the generating polynomial system. At some discrete instants of the observer’s proper time, mergers and subsequent transmutations of a pair of particles-roots take place, thus simulating the processes of annihilation/creation of a particle/antiparticle pair.
Kinematic Censorship as a Constraint on Allowed Scenarios of High-Energy Particle Collisions
摘要
In the recent years, it was found that the energy Ec.m. in the center of mass frame of two colliding particles can be unbounded near black holes. If a collision occurs precisely on the horizon, Ec.m. is formally infinite. However, in any physically reasonable situation this is impossible. We collect different scenarios of this kind and show why in every act of collision Ec.m. is indeed finite (although it can be as large as one likes). The factors preventing an infinite energy are diverse: the necessity of infinite proper time, infinite tidal forces, potential barrier, etc. This prompts us to formulate a general principle according to which the limits in which Ec.m.→ 8 are never achieved. We call this the kinematic censorship (KC). Although by itself the validity of KC is quite natural, its application allows one to forbid scenarios of collisions predicting infinite Ec.m. without going into details. The KC is valid even in the test particle approximation, so an explanation of why Ec.m. cannot be infinite does not require references (common in the literature) to a nonlinear regime, back-reaction, etc. The KC remains valid not only for freely moving particles but also if particles are subject to a finite force. For an individual particle, we consider a light-like continuous limit of a timelike trajectory in which the effective mass turns to zero. We show that it cannot be accelerated to an infinite energy during a finite proper time under the action of such a force. As an example, we consider the dynamics of a scalar particle interacting with a background scalar field.
Particle Creation in Friedmann–Robertson–Walker Universe
摘要
Using variable gravitational and cosmological constants, the mechanism of particle creation in the universe is studied for Friedmann–Robertson–Walker (FRW) space-times at high dimensions to explain the early deceleration and present accelerating phases. To investigate the dynamics of these phases, we consider two scale factor of the forms \(a(t)=\sqrt{t^\alpha{e^t}}\) and \(a(t)=\sqrt[m]{{\rm{sin}}h(kt)}\), which yield two different time-dependent deceleration parameters. Firstly, we modify the d-dimensional time-dependent field equations, including the general formulation of particle creation and entropy generation mechanisms. Then, we investigate the time dependence of a few quantities such as the particle creation rate ψ, the entropy S, the gravitational constant G, the cosmological constant Λ, the energy density ρ, the deceleration parameter q, etc. We show that all constants and quantities, except the gravitational constant G and the entropy S, characteristically decrease with time for two kinds of scale factors in all dimensions. However, the gravitational constant G and the entropy S increase with time. Additionally, we show that the cosmological constant Λ is unexpectedly independent of the particle creation mechanism, unlike G.