Wave function of the Universe in the early stage of its evolution (original) (raw)
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Quantum relativistic cosmology: Dynamical interpretation and tunneling universe
International Journal of Modern Physics D, 2020
In this work, the wave functions associated to the quantum relativistic universe, which is described by the Wheeler–DeWitt equation, are obtained. Taking into account different kinds of energy density, namely, matter, radiation, vacuum, dark energy and quintessence, we discuss some aspects of the quantum dynamics. In all these cases, the wave functions of the quantum relativistic universe are given in terms of the triconfluent Heun functions. We investigate the expansion of the universe using these solutions and found that the asymptotic behavior for the scale factor is [Formula: see text] for whatever the form of energy density is. On the other hand, we analyze the behavior at early stages of the universe and found that [Formula: see text]. We also calculate and analyze the transmission coefficient through the effective potential barrier.
Some exact results on quantum relativistic cosmology: dynamical interpretation and tunneling phase
arXiv: General Relativity and Quantum Cosmology, 2019
In this work the wave functions associated to the quantum relativistic universe, which is described by the Wheeler-DeWitt equation, are obtained. Taking into account all forms of energy density, namely, matter, radiation, vacuum, dark energy, and quintessence, we discuss some aspects of the quantum dynamics. In all these cases, the wave functions of the quantum relativistic universe are given in terms of the triconfluent Heun functions. We investigate the expansion of the universe using these solutions and found that the asymptotic behavior for the scale factor is a(t)simmboxeta(t) \sim \mbox{e}^{t}a(t)simmboxet for whatever the form of energy density is. On the other hand, we analyze the behavior at early stages of the universe and found that a(t)simt1/2a(t) \sim t^{1/2}a(t)simt1/2. We also calculate and analyze the transmission coefficient through the effective potential barrier.
Origin of the Universe as a quantum tunneling event
Physical Review D, 1982
We present a nonsingular model of cosmogenesis in which the Universe arises as a result of quantum-mechanical barrier penetration. The Universe is described throughout its evolution by a Friedmann-Robertson-Walker (FRW) metric, and the matter distribution by a perfect fiuid, whose equation of state is chosen so as to allow the tunneling to occur. Cosmic evolution proceeds in three stages; an initial static spacetime configuration tunnels into a "fireball" state in which particle creation occurs. As the fireball expands, particle creation ends, and the Universe enters the "post-big-bang" epoch of adiabatic expansion. We find that within the context of the FRW ansatz, only a spatially closed universe may originate in this manner. Implications of this creation scheme and possible generalizations are discussed. As a by-product of this investigation we find that the evolution of the Universe is described by a Gell-Manu-Low equation with the P function specified by the equation of state.
A Fully Quantum Model of Big Bang
Theoretical Concepts of Quantum Mechanics, 2012
and some discussions in Refs. with references therein). Today, among all variety of models one can select two approaches which are the prevailing ones: these are the Feynman formalism of path integrals in multidimensional spacetime, developed by the Cambridge group and other researchers, called the "Hartle-Hawking method" (for example, see Ref. ), and a method based on direct consideration of tunneling in 4-dimensional Euclidian spacetime, called the "Vilenkin method" (for example, see Refs. ). Here, in the quantum approach we have the following picture of the Universe creation: a closed Universe with a small size is formed from "nothing" (vacuum), where by the word "nothing" one refers to a quantum state without classical space and time. A wave function is used for a probabilistic description of the creation of the Universe and such a process is connected with transition of a wave through an effective barrier. Determination of penetrability of this barrier is a key point in the estimation of duration of the formation of the Universe, and the dynamics of its expansion in the first stage. However, in the majority of these models, with the exception of some exactly solvable models, tunneling is mainly studied in details in the semiclassical approximation (see Refs. (Rubakov, 1999;). An attractive side of such an approach is its simplicity in the construction of decreasing and increasing partial solutions for the wave function in the tunneling region, the outgoing wave function in the external region, and the possibility to define and to estimate in an enough simply way the penetrability of the barrier, which can be used to obtain the duration of the nucleation of the Universe. The tunneling boundary condition
The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and A &0. The ground state corresponds to de Sitter space in the classical limit.
Resonant structure of the early-universe space-time
The European Physical Journal Plus, 2011
A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes of wave function, penetrability T bar and reflection R bar relatively the barrier (accuracy of the method: |T bar + R bar − 1| < 1 · 10 −15 ), coefficient of penetration (i. e. probability of the packet to penetrate from the internal well outside with its tunneling), coefficient of oscillations (describing oscillating behavior of the packet inside the internal well). Using the method, evolution of universe in the closed Friedmann-Robertson-Walker model with quantization in presence of positive cosmological constant, radiation and component of generalize Chaplygin gas is studied. It is established (for the first time): (1) oscillating dependence of the penetrability on localization of start of the packet; (2) presence of resonant values of energy of radiation E rad , at which the coefficient of penetration increases strongly. From analysis of these results it follows: (1) necessity to introduce initial condition into both non-stationary, and stationary quantum models; (2) presence of some definite values for the scale factor a, where start of expansion of universe is the most probable; (3) during expansion of universe in the initial stage its radius is changed not continuously, but passes consequently through definite discrete values and tends to continuous spectrum in latter time.
The wave function of the universe
1994
List of figures IX 8 Wormholes in Superspace 8.1 Exact HP wormhole states 8.2 Wormhole Representation 8.3 Quantum Wormholes. .. 8.3.1 The minimally coupled massive scalar field 8.4 The power-law potential 2 Kq 2 q.
Quantum dynamics of evolution of flat universe in the first stage
2013
Process of formation of the universe with its further expansion in the first evolution stage is investigated in the framework of Friedmann-Robertson-Walker metrics on the basis of quantum model, where a new type of matter is introduced, which energy density is dependent on velocity of the expansion. It is shown that such an improvement of the model forms potential barrier for the flat universe at k=0k=0k=0 (in contrast with generalized Chaplygin gas model). Peculiarities of wave function are analyzed in details, which is calculated by fully quantum (non-semiclassic) approach, for the different barrier regions and stages of evolution. Resonant influence of the initial and boundary conditions on the barrier penetrability is shown (in contrast with Vilenkin and Hawking approaches). In order to perform a comparative analysis, how much quickly the universe is expanded by different models, new quantum definitions of velocity and Hubble function are introduced. These notions allow us to study dynamics of evolution of universe in quantum cosmology both in the first stage, and in later times.
Tunneling of the Closed Friedmann Universe with Generation of Scalar Waves
2001
The evolution of the closed Friedmann Universe with a packet of short scalar waves is considered with the help of the Wheeler–DeWitt equation. The packet ensures conservation of homogeneity and isotropy of the metric on average. It is shown that during tunneling the amplitudes of short waves of a scalar field can increase catastrophically promptly if their influence to the
A QUANTUM APPROACH TO RELATIVISTIC COSMOLOGY
Cosmology is the branch of astrophysics concerned with the large-scale structure of the cosmos and (in the current interpretation) the origin of the universe. Yet the scientific method employed in other branches of physics consists in equating the origins of the constituents of the physical world-the particles and fields that appear in it-to the ends of other elements: science seeks to explain the world from a principle of conservation. It thus appears incongruous that an explanation of the large-scale structure of the universe should require the addition of another "origin", that of the universe as a whole. If the universe had a beginning, then matter and motion, space and time, had to be created. This point of view is obviously incompatible with a principle of conservation. A model that is consistent with the conservation principle, and therefore requires no cosmic beginning, can be investigated by examining the current conception of the large-scale structure of space and time in the light of physical theory. Analysis reveals that the conservation-violating universe model contradicts other theoretical principles which have received confirmation from empirical measurement. An alternative model is proposed to circumvent these difficulties, and an extension of general relativity theory is posited. ================================================================== Cosmology in the twentieth century has been dominated by two major advances: one observational, the other theoretical. The former-the discovery that the spectral lines of light emitted by external galaxies were shifted toward the red in proportion to distance-constitutes the primary empirical foundation for a cosmological model. How this correspondence between redshift and distance is interpreted in the light of theory determines the model. Astronomers presently acknowledge that a universe model must be predicated upon the analytical framework established by the second scientific advance-the general theory of relativity. But unlike the present model for cosmology, relativity unambiguously retains a conservation theorem for momentum and energy. If the accepted universe model is found to exhibit further inconsistencies with relativity, then it is necessary to abandon this model in favour of one that concurs rigorously with theoretical principles.