Quantum geometrodynamics: The path integral and the initial value problem for the wave function of the universe

1986 ◽  
Vol 167 (3) ◽  
pp. 289-294 ◽  
Author(s):  
A.O. Barvinsky ◽  
V.N. Ponomariov
Keyword(s):  
Wave Function ◽  
Path Integral ◽  
Initial Value Problem ◽  
Initial Value ◽  
The Universe ◽  
Quantum Geometrodynamics

scholarly journals Fuzzy Instantons in Landscape and Swampland: Review of the Hartle–Hawking Wave Function and Several Applications

Universe ◽  
2021 ◽  
Vol 7 (10) ◽  
pp. 367
Author(s):  
Dong-han Yeom
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
Path Integral ◽  
Initial Conditions ◽  
Black Hole Physics ◽  
Slow Roll ◽  
Potential Shape ◽  
Euclidean Wormholes ◽  
The Universe ◽  
Origin Of The Universe

The Euclidean path integral is well approximated by instantons. If instantons are dynamical, they will necessarily be complexified. Fuzzy instantons can have multiple physical applications. In slow-roll inflation models, fuzzy instantons can explain the probability distribution of the initial conditions of the universe. Although the potential shape does not satisfy the slow-roll conditions due to the swampland criteria, the fuzzy instantons can still explain the origin of the universe. If we extend the Euclidean path integral beyond the Hartle–Hawking no-boundary proposal, it becomes possible to examine fuzzy Euclidean wormholes that have multiple physical applications in cosmology and black hole physics.

scholarly journals THE WAVE FUNCTION OF THE UNIVERSE BY THE NEW EUCLIDEAN PATH-INTEGRAL APPROACH IN QUANTUM COSMOLOGY

1993 ◽  
Vol 02 (02) ◽  
pp. 249-256 ◽  
Author(s):  
ATUSHI ISHIKAWA ◽  
HARUHIKO UEDA
Keyword(s):  
Wave Function ◽  
Path Integral ◽  
Regularization Method ◽  
Positive Definite ◽  
Integral Approach ◽  
Type I ◽  
Path Integral Approach ◽  
The Universe ◽  
Friedmann Robertson Walker ◽  
Hilbert Action

The wave function of the universe is evaluated by using the Euclidean path integral approach. As is well known, the real Euclidean path integral diverges because the Einstein-Hilbert action is not positive definite. In order to obtain a finite wave function, we propose a new regularization method and calculate the wave function of the Friedmann-Robertson-Walker type minisuperspace model. We then consider a homogeneous but anisotropic type minisuperspace model, which is known as the Bianch type I model. The physical meaning of the wave function by this new regularization method is also examined.

On the meaning of the wave function of the Universe

2019 ◽  
Vol 28 (13) ◽  
pp. 1941009 ◽  
Author(s):  
Tatyana P. Shestakova
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Quantum Processes ◽  
Extended Phase ◽  
Quantization Of Gravity ◽  
Present Universe ◽  
Objective Description ◽  
The Universe ◽  
Quantum Geometrodynamics ◽  
Space Approach

The meaning of the wave function of the Universe was actively discussed in 1980s. In most works on quantum cosmology, it is accepted that the wave function is a probability amplitude for the Universe to have some space geometry, or to be found in some point of the Wheeler superspace. It seems that the wave function gives maximally objective description compatible with quantum theory. However, the probability distribution does not depend on time and does not take into account the existing of our macroscopic evolving Universe. What we wish to know is how quantum processes in the Early Universe determined the state of the present Universe in which we are able to observe macroscopic consequences of these quantum processes. As an alternative to the Wheeler–DeWitt quantum geometrodynamics, we consider the picture that can be obtained in the extended phase space approach to quantization of gravity. The wave function in this approach describes different states of the Universe which correspond to different stages of its evolution.

scholarly journals A STUDY OF KANTOWSKI–SACHS MODEL IN ASHTEKAR VARIABLES

1998 ◽  
Vol 13 (28) ◽  
pp. 4931-4937 ◽  
Author(s):  
SUBENOY CHAKRABORTY ◽  
NABAJIT CHAKRAVARTY
Keyword(s):  
Wave Function ◽  
Path Integral ◽  
Quantum Cosmology ◽  
Cosmological Term ◽  
Classical Solutions ◽  
Integral Formalism ◽  
Path Integral Formalism ◽  
Ashtekar Variables ◽  
The Universe

In this paper we study classical and quantum cosmology in Kantowski–Sachs model using Ashtekar variables. Classical solutions are obtained for the above model with a cosmological term and Hamilton–Jacobi (HJ) equations have been studied to obtain inflationary solutions. In quantum cosmology, the wave function of the Universe is obtained using path integral formalism as well as by solving the Wheeler–DeWitt (WD) equation.

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