“Stationary” Schrödinger equation in quantum cosmology

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040040
Author(s):  
N. Gorobey ◽  
A. Lukyanenko ◽  
A. Shavrin

The conditional principle of extremum in quantum cosmology is formulated for a positive functional of the energy density of space, in which gravitational constraints serve as additional conditions. The extremum conditions determine the discrete spectrum of the “stationary” state of the universe with the corresponding values of the energy density of space. A dynamic interpretation of solutions is proposed, in which the quantum number of the energy density plays the role of cosmic time. In the self-consistent harmonic approximation, the quantum dynamics of the anisotropic model of the Bianchi IX universe is considered.

Author(s):  
Alex Hankey

Higher states of consciousness are developed by meditation, defined by Patanjali as that which transforms focused attention into pure consciousness, the 4th state of pure consciousness - a major state in its own right, with its own physics, that of ‘experience information'. Phenomenologies of states 5 to 7 are explained from the perspective of modern physics and quantum cosmology. The role of the 5th state in life is to make possible witnessing states 1 to 3 resulting in ‘Perfection in Action'. Refinement of perception involved in the 6th State results in hearing the Cosmic Om, seeing the Inner Light, and seventh sense perception. All require special amplification processes on pathways of perception. Unity and Brahman Consciousness and their development are discussed with examples from the great sayings of the Upanishads, and similar cognitions like those of poet, Thomas Traherne. Throughout, supporting physics is given, particularly that of experience information, and its implications for Schrodinger's cat paradox and our scientific understanding of the universe as a whole.


1993 ◽  
Vol 02 (02) ◽  
pp. 221-247 ◽  
Author(s):  
E.I. GUENDELMAN ◽  
A.B. KAGANOVICH

We consider 1+D-dimensional, toroidally compact Kaluza-Klein theories. In the context of the minisuperspace approach of quantum cosmology, we solve the Wheeler-DeWitt equation in the presence of a negative cosmological constant and dust. Then, it is found that the quantum effects stabilize the volume of the Universe, so that there can be an avoidance of the cosmological singularity. Although cosmic time does not appear explicitly in the Wheeler-DeWitt equation, we find that a cosmic time dependence appears for the expectation values of certain variables. This result is obtained when proper care of some subtle points concerning the definition of averages in this model is taken. The stabilization of the volume, when there is anisotropy in the evolution of the Universe (which turns out to be quantized), is consistent with another effect we find: the existence of a “quantum inflationary phase” for some dimensions and simultaneously the existence of a “quantum deflationary contraction” for the rest.


2014 ◽  
Vol 789 (2) ◽  
pp. 96 ◽  
Author(s):  
Hakim Atek ◽  
Jean-Paul Kneib ◽  
Camilla Pacifici ◽  
Matthew Malkan ◽  
Stephane Charlot ◽  
...  

2019 ◽  
Vol 34 (34) ◽  
pp. 1950283 ◽  
Author(s):  
Saumya Ghosh ◽  
Sunandan Gangopadhyay ◽  
Prasanta K. Panigrahi

In this paper, we perform the Wheeler–DeWitt quantization for Bianchi type I anisotropic cosmological model in the presence of a scalar field minimally coupled to the Einstein–Hilbert gravity theory. We also consider the cosmological (perfect) fluid to construct the matter sector of the model whose dynamics plays the role of time. After obtaining the Wheeler–DeWitt equation from the Hamiltonian formalism, we then define the self-adjointness relations properly. Doing that, we proceed to get a solution for the Wheeler–DeWitt equation and construct a well-behaved wave function for the universe. The wave packet is next constructed from a superposition of the wave functions with different energy eigenvalues together with a suitable weight factor which renders the norm of the wave packet finite. It is then concluded that the Big-Bang singularity can be removed in the context of quantum cosmology.


2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641014 ◽  
Author(s):  
Natalia Gorobey ◽  
Alexander Lukyanenko

We find a physical state of a closed universe with the minimal excitation of the universe expansion energy in quantum gravity. It is an analog of the vacuum state of the ordinary quantum field theory in the Minkowsky space, but in our approach an energy of space of a closed universe together with the energy of its matter content are minimized. This ground state is chosen among an enlarged set of physical states, compared with the ordinary covariant quantum gravity. In our approach, physical states are determined by weak constraints: quantum mechanical averages of gravitational constraint operators equal zero. As a result, they appear to be non-static in such a modification of quantum gravity. Quantum dynamics of the universe is described by Schrödinger equation with a cosmic time determined by weak gravitational constraints. In order to obtain the observed megascopic universe with the inflation stage just after its quantum beginning, a lot of the energy in the form of the inflaton scalar field condensate is prescribed to the initial state. Parameters of the initial state for a homogeneous model of the universe are calculated.


2018 ◽  
Vol 63 (3) ◽  
pp. 196
Author(s):  
V. E. Kuzmichev ◽  
V. V. Kuzmichev

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 one of the universe (the domain of 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 a sign of the quantum correction to the pressure is discussed.


2021 ◽  
Vol 4 (3) ◽  

The Cosmic Time Hypothesis (CTH) presented in this paper is a purely axiomatic theory. In contrast to today's standard model of cosmology, the ɅCDM model, it does not contain empirical parameters such as the cosmological constant Ʌ, nor does it contain sub-theories such as the inflation theory. The CTH was developed solely on the basis of the general theory of relativity (GRT), aiming for the greatest possible simplicity. The simplest cosmological model permitted by ART is the Einstein-de Sitter model. It is the basis for solving some of the fundamental problems of cosmology that concern us today. First of all, the most important results of the CTH: It solves one of the biggest problems of cosmology the problem of the cosmological constant (Ʌ)-by removing the relation between and the vacuum energy density ɛv (Λ=0, ɛv > 0). According to the CTH, the vacuum energy density ɛv is not negative and constant, as previously assumed, but positive and time-dependent (ɛv ̴ t -2). ɛv is part of the total energy density (Ɛ) of the universe and is contained in the energy-momentum tensor of Einstein's field equations. Cosmology is thus freed from unnecessary ballast, i.e. a free parameter (= natural constant) is omitted (Ʌ = 0). Conclusion: There is no "dark energy"! According to the CTH, the numerical value of the vacuum energy density v is smaller by a factor of ≈10-122 than the value calculated from quantum field theory and is thus consistent with observation. The measurement data obtained from observations of SNla supernovae, which suggest a currently accelerated expansion of the universe, result - if interpreted from the point of view of the CTH - in a decelerated expansion, as required by the Einstein-de Sitter universe. Dark matter could also possibly not exist, because the KZH demands that the "gravitational constant" is time-dependent and becomes larger the further the observed objects are spatially and thus also temporally distant from us. Gravitationally bound local systems, e.g. Earth - Moon or Sun - Earth, expand according to the same law as the universe. This explains why Hubble's law also applies within very small groups of galaxies, as observations show. The CTH requires that the strongest force (strong nuclear force) and the weakest (gravitational force) at Planck time (tp ≈10-43 seconds after the "big bang") when all forces of nature are supposed to have been united in a single super force, were of equal magnitude and had the same range. According to the KZH, the product of the strength and range of the gravitational force is constant, i.e. independent of time, and is identical to the product of the strength and range of the strong nuclear force. At Planck time, the universe had the size of an elementary particle (Rp = rE ≈10-15 m). This value also corresponds to the range of the strong nuclear force (Yukawa radius) and the Planck length at Planck time. The CTH provides a possible explanation for Mach's first and second principles. It solves some old problems of the big bang theory in a simple and natural way. The problem of the horizon, flatness, galaxy formation and the age of the world. The inflation theory thus becomes superfluous. • The CTH provides the theoretical basis for the theory of Earth expansion • In Cosmic Time, there was no Big Bang. The universe is infinitely old. • Unlike other cosmological models, the CTH does not require defined "initial conditions" because there was no beginning. • The CTH explains why the cosmic expansion is permanently in an unstable state of equilibrium, which is necessary for a long-term flat (Euclidean), evolutionarily developing universe.


2020 ◽  
Vol 498 (2) ◽  
pp. 2544-2553
Author(s):  
I Horvath ◽  
D Szécsi ◽  
J Hakkila ◽  
Á Szabó ◽  
I I Racz ◽  
...  

ABSTRACT The Hercules–Corona Borealis Great Wall is a statistically significant clustering of gamma-ray bursts (GRBs) around redshift 2. Motivated by recent theoretical results indicating that a maximal Universal structure size may indeed coincide with its estimated size (2–3 Gpc), we reexamine the question of this Great Wall’s existence from both observational and theoretical perspectives. Our statistical analyses confirm the clustering’s presence in the most reliable data set currently available, and we present a video showing what this data set looks like in 3D. Cosmological explanations (i.e. having to do with the distribution of gravitating matter) and astrophysical explanations (i.e. having to do with the rate of star formation over cosmic time and space) regarding the origin of such a structure are presented and briefly discussed and the role of observational bias is also discussed at length. This, together with the scientific importance of using GRBs as unique cosmological probes, emphasises the need for future missions such as the THESEUS satellite, which will provide us with unprecedentedly homogeneous data of GRBs with measured redshifts. We conclude from all this that the Hercules–Corona Borealis Great Wall may indeed be the largest structure in the Universe – but to be able to decide conclusively whether it actually exists, we need THESEUS.


Author(s):  
S. L. Cherkas ◽  
V. L. Kalashnikov

Five-vectors theory of gravity is proposed, which admits an arbitrary choice of the energy density reference level. This theory is formulated as the constraint theory, where the Lagrange multipliers turn out to be restricted to some class of vector fields unlike the General Relativity (GR), where they are arbitrary. A possible cosmological implication of the proposed model is that the residual vacuum fluctuations dominate during the whole evolution of the universe. That resembles the universe having a nearly linear dependence of a scale factor on cosmic time.


1994 ◽  
Vol 09 (13) ◽  
pp. 1141-1150 ◽  
Author(s):  
E.I. GUENDELMAN ◽  
A.B. KAGANOVICH

In many interesting models, including superstring theories, a vacuum with negative cosmological constant is predicted. For quantum cosmology (in higher dimensions) in the presence of coherent dilaton excitations and a negative cosmological constant, the role of cosmic time can be understood and we can then predict the existence of a “quantum inflationary phase” for some dimensions and a simultaneous “quantum deflationary phase” for the remaining dimensions. We discuss qualitatively how it may be possible to exit from this inflation-compactification era and give an example which involves a transition to a phase with zero cosmological constant which allows a classical description at late times.


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