Tomographic analysis of quantum and classical de Sitter cosmological models

2019 ◽  
Vol 28 (16) ◽  
pp. 2040009 ◽  
Author(s):  
Cosimo Stornaiolo
Keyword(s):  
Quantum Cosmology ◽  
Classical Limit ◽  
Initial Conditions ◽  
Quantum Tomography ◽  
Wave Functions ◽  
Hamiltonian Constraint ◽  
De Sitter ◽  
Quantum Universe ◽  
Tomographic Analysis ◽  
The Universe

In this work, we show the importance of introducing the quantum tomography formalism to analyze the properties of wave functions in quantum cosmology. In particular, we examine the initial conditions of the universe proposed by various authors in the context of de Sitter’s cosmology studying their classical limit and comparing it with the classical tomogram obtained from the Hamiltonian constraint in General Relativity. This comparison gives us the opportunity to find under which conditions there is a transition from the quantum universe to the classical one. A relevant result is that in these models the decay of the cosmological constant is a sufficient condition for this transition.

scholarly journals Tomographic analysis of the de Sitter model in quantum and classical cosmology

2019 ◽  
Vol 16 (01) ◽  
pp. 1950012 ◽  
Author(s):  
Cosimo Stornaiolo
Keyword(s):  
Quantum Cosmology ◽  
Initial Conditions ◽  
Classical Mechanics ◽  
Planck Scale ◽  
De Sitter ◽  
Classical Transition ◽  
Sitter Model ◽  
Tomographic Analysis ◽  
Tomographic Representation ◽  
De Sitter Model

The importance of the tomographic approach is that either in quantum mechanics as in classical mechanics the state of a physical system is expressed with marginal probability functions called tomograms. The extension of this procedure to quantum cosmology is straightforward. But in this paper, instead of using the tomographic representation, we use tomograms to analyze the properties of the quantum and classical universes, starting from the wave functions in quantum cosmology and from the phase space distributions in classical cosmology. In this, there is a part where we resume the properties of the tomograms. Then, we apply them to study and discuss the properties of the initial conditions introduced by Hartle and Hawking, Vilenkin and Linde and finally we argue about their classical transition. According to the results of this paper it follows that the decay of the cosmological constant from the Planck scale to the present one could be responsible for the transition of the quantum universe to the classical one.

Exact solutions for scalar field cosmology in f(R) gravity

2017 ◽  
Vol 32 (30) ◽  
pp. 1750164 ◽  
Author(s):  
S. D. Maharaj ◽  
R. Goswami ◽  
S. V. Chervon ◽  
A. V. Nikolaev
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Scalar Curvature ◽  
Evolution Equations ◽  
Initial Conditions ◽  
De Sitter ◽  
Airy Functions ◽  
Special Cases ◽  
The Universe ◽  
Current Stage

We study scalar field FLRW cosmology in the content of f(R) gravity. Our consideration is restricted to the spatially flat Friedmann universe. We derived the general evolution equations of the model, and showed that the scalar field equation is automatically satisfied for any form of the f(R) function. We also derived representations for kinetic and potential energies, as well as for the acceleration in terms of the Hubble parameter and the form of the f(R) function. Next we found the exact cosmological solutions in modified gravity without specifying the f(R) function. With negligible acceleration of the scalar curvature, we found that the de Sitter inflationary solution is always attained. Also we obtained new solutions with special restrictions on the integration constants. These solutions contain oscillating, accelerating, decelerating and even contracting universes. For further investigation, we selected special cases which can be applied with early or late inflation. We also found exact solutions for the general case for the model with negligible acceleration of the scalar curvature in terms of special Airy functions. Using initial conditions which represent the universe at the present epoch, we determined the constants of integration. This allows for the comparison of the scale factor in the new solutions with that for current stage of the universe evolution in the [Formula: see text]CDM model.

scholarly journals The Asymmetric Cosmic Time – The Key to a New Cosmological Model

2020 ◽  
Vol 2 (1) ◽  
pp. 97-111
Author(s):  
Horst Fritsch ◽  
Eberhard Schluecker
Keyword(s):  
Cosmological Model ◽  
Initial Conditions ◽  
Logical Consequence ◽  
Cosmic Time ◽  
Big Bang ◽  
Relativity Theory ◽  
Accelerated Expansion ◽  
Theory Of Relativity ◽  
De Sitter ◽  
The Universe

The asymmetric cosmic time is a logical consequence of the General Theory of Relativity (GR), if one demands that it should apply to the entire cosmos. From the simplest cosmological model that is consistent with the ART (Einstein-de Sitter model) thus follows the < Cosmic Time Hypothesis > (CTH), which offers solutions for many unsolved problems of cosmology that the current standard model of cosmology (ɅCDM model) cannot explain. According to the CTH, space, time and matter form a unit and develop evolutionarily according to identical, time-dependent laws. According to the CTH time has neither beginning nor end. The "big bang" disappears into the infinite past, which is why the universe manages without inflation. The accelerated expansion of the universe is also unlikely to occur if the SN-Ia measurement results are interpreted using the CTH. The cosmological constant Ʌ can then be omitted (Ʌ=0) and consequently no "dark energy" is needed. In addition, the CTH also provides interesting results on the topics: Initial conditions for hypotheses, stability of the expanding, flat universe (Ω=1), cosmic energy balance (is there negative energy ?), theory of earth expansion, unification of natural forces, Mach's principle. Should the CTH receive broad experimental confirmation, the GR could be extended to the "Universal Relativity Theory" (UR).

QUANTUM COSMOLOGY IN ANISOTROPIC COSMOLOGICAL MODELS WITH SCALAR–TENSOR THEORIES

2001 ◽  
Vol 10 (06) ◽  
pp. 943-956
Author(s):  
SUBENOY CHAKRABORTY
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Classical Limit ◽  
Cosmological Models ◽  
Integral Formulation ◽  
Causal Interpretation ◽  
Anisotropic Cosmological Models ◽  
Bohmian Trajectories ◽  
The Universe ◽  
Method Of Steepest Descent

This paper deals with quantum cosmological phenomena in anisotropic cosmological models with nonminimally coupled scalor field. With proper transformation of the field variables, the Wheeler–Dewitt (WD) equation looks simple in form and solutions are obtained using separable form of the wave function. Using part integral formulation, the wave function of the Universe has been evaluated by the method of steepest descent. Finally, the causal interpretation has been done using quantum Bohmian trajectories and also we study the classical limit of some particular solutions of these quantum models.

Gibbons–Hawking temperature corrected by quantum cosmology

2017 ◽  
Vol 26 (10) ◽  
pp. 1750116 ◽  
Author(s):  
Je-An Gu ◽  
Sang Pyo Kim ◽  
Che-Min Shen
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Quantum Correction ◽  
Planck Scale ◽  
Friedmann Equation ◽  
Back Reaction ◽  
De Sitter ◽  
Pure Gravity ◽  
The Universe ◽  
Spacetime Fluctuations

We explore a quantum cosmology description of the de Sitter (dS) radiation and its back-reaction to a dS space, inherent in the wave function of the Wheeler–DeWitt equation for pure gravity with a cosmological constant. We first investigate the quantum Friedmann–Lemaitre–Robertson–Walker cosmological model and then consider the possible effects of inhomogeneities of the universe on the dS radiation. In both the cases we obtain the modified Friedmann equation, including the back-reaction from spacetime fluctuations, and the quantum-corrected Gibbons–Hawking (GH) temperature. It is shown that the quantum correction increases the GH temperature with the increment characterized by the ratio of the dS scale to the Planck scale.

scholarly journals The perturbed universe in the deformed algebra approach of loop quantum cosmology

2016 ◽  
Vol 25 (08) ◽  
pp. 1642003 ◽  
Author(s):  
Julien Grain
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Initial Conditions ◽  
Power Spectra ◽  
Quantum Corrections ◽  
Loop Quantum Cosmology ◽  
Algebra Approach ◽  
Deformed Algebra ◽  
Contracting Phase ◽  
The Universe

Loop Quantum Cosmology (LQC) is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical spacetime is inspired by Loop Quantum Gravity (LQG) ideas. In addition, LQC could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modelings in the light of observations. To do so however, modeling both the background evolution and its perturbations is needed. The latter described cosmic inhomogeneities that are the main cosmological observables. In this context, we present the so-called deformed algebra approach implementing the quantum corrections to the perturbed universe at an effective level by taking great care of gauge issues. We particularly highlight that in this framework, the algebra of hypersurface deformation receives quantum corrections, and we discuss their meaning. The primordial power spectra of scalar and tensor inhomogeneities are then presented, assuming initial conditions are set in the contracting phase preceding the quantum bounce and the well-known expanding phase of the cosmic history. These spectra are subsequently propagated to angular power spectra of the anisotropies of the cosmic microwave background. It is then shown that regardless of the choice for the initial conditions inside the effective approach for the background evolution (except that they are set in the contracting phase), the predicted angular power spectra of the polarized [Formula: see text]-modes exceed the upper bound currently set by observations. The exclusion of this specific version of LQC establishes the falsifiability of the approach, though one shall not conclude here that either LQC or LQG excluded.

scholarly journals Swampland constraints on no-boundary quantum cosmology

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hiroki Matsui ◽  
Takahiro Terada
Keyword(s):  
Scalar Potential ◽  
Expanding Universe ◽  
De Sitter ◽  
Positive Power ◽  
Order Unity ◽  
Eternal Inflation ◽  
Quantum Universe ◽  
Point Solution ◽  
Negligible Probability ◽  
The Universe

Abstract The Hartle-Hawking no-boundary proposal describes the quantum creation of the universe. To have a non-negligible probability to obtain a classical expanding universe, eternal inflation is required, which is severely constrained by Swampland conjectures such as the refined de Sitter conjecture and the distance conjecture. We discuss this issue in detail and demonstrate the incompatibility. We show that the dimensionless parameters in the refined de Sitter conjecture should be bounded from above by a positive power of the scalar potential to realize the classical expanding universe. In other words, the probability of the classical expanding universe is extremely small under the Swampland conjectures unless the parameters are much smaller than unity. If they are order unity, on the other hand, the saddle-point solution itself ceases to exist implying a genuinely quantum universe.

scholarly journals Preinflationary Dynamics of Power-Law Potential in Loop Quantum Cosmology †

Universe ◽  
2018 ◽  
Vol 4 (8) ◽  
pp. 87 ◽  
Author(s):  
M. Shahalam
Keyword(s):  
Quantum Cosmology ◽  
Initial Conditions ◽  
Big Bang ◽  
Loop Quantum Cosmology ◽  
Inflationary Universe ◽  
Slow Roll ◽  
Wide Range ◽  
The Big Bang ◽  
The Universe ◽  
Big Bang Singularity

In this article, I mainly discuss the dynamics of the pre-inflationary Universe for the potential V ( ϕ ) ∝ ϕ n with n = 5 / 3 in the context of loop quantum cosmology, in which the big bang singularity is resolved by a non-singular quantum bounce. In the case of the kinetic energy-dominated initial conditions of the scalar field at the bounce, the numerical evolution of the Universe can be split up into three regimes: bouncing, transition, and slow-roll inflation. In the bouncing regime, the numerical evolution of the scale factor does not depend on a wide range of initial values, or on the inflationary potentials. I calculate the number of e-folds in the slow-roll regime, by which observationally identified initial conditions are obtained. Additionally, I display the phase portrait for the model under consideration.

scholarly journals DOES QUANTUM COSMOLOGY PREDICT A CONSTANT DILATONIC FIELD?

2005 ◽  
Vol 14 (02) ◽  
pp. 291-307 ◽  
Author(s):  
F. G. ALVARENGA ◽  
A. B. BATISTA ◽  
J. C. FABRIS
Keyword(s):  
Cosmological Model ◽  
Quantum Cosmology ◽  
Initial Conditions ◽  
Specific Model ◽  
Scale Factor ◽  
Gravitational Coupling ◽  
Expectation Values ◽  
Time Coordinate ◽  
Classical Models ◽  
The Universe

Quantum cosmology may permit to determine the initial conditions of the Universe. In particular, it may select a specific model between many possible classical models. In this work, we study a quantum cosmological model based on the string effective action coupled to matter. The Schutz's formalism is employed in the description of the fluid. A radiation fluid is considered. In this way, a time coordinate may be identified and the Wheeler–DeWitt equation reduces in the minisuperspace to a Schrödinger-like equation. It is shown that, under some quite natural assumptions, the expectation values indicate a null axionic field and a constant dilatonic field. At the same time the scale factor exhibits a bounce revealing a singularity-free cosmological model. In some cases, the mininum value of the scale factor can be related to the value of gravitational coupling.

scholarly journals On space and time in quantum cosmology

2002 ◽  
Vol 2 (4) ◽  
pp. 173-182 ◽  
Author(s):  
Ljubisa Nesic ◽  
Stojan Obradovic
Keyword(s):  
Quantum Cosmology ◽  
De Sitter ◽  
Real Numbers ◽  
Standard Quantum ◽  
Space And Time ◽  
Sitter Model ◽  
Basic Ideas ◽  
The Universe ◽  
Early Phases ◽  
De Sitter Model

The paper considers the properties of space and time in quantum cosmology. It presented the basic ideas of the substantial and relational conceptions of space and time, as well the basic ideas of the continuity and discreteness of space and time. The basics of standard quantum cosmology, i.e. quantum cosmology formulated over the field of real numbers R, have also been presented. Quantum cosmology is the application of the quantum theory to the universe as a whole in the early phases of its evolution, when the universe was very small so that all the four interactions were practically unified. In order to obtain the maximum possible information from quantum cosmology it is necessary that it be "complete". The concept "complete" refers here to the formulation of the theory over the field of real numbers and the field of p-adic numbers Qp. Since p-adic numbers are generally not well-known, the idea of their introduction has carefully been considered. Within the p-adic quantum cosmology representing quantum cosmology over the field of p-adic numbers Qp, the main results concerning the de Sitter model have been presented. The consequence of this (complete) formulation of the de Sitter model is the radius discreteness of the universe.

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