Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics D

Tomographic analysis of quantum and classical de Sitter cosmological models

C. Stornaiolo

Published Sep 16, 2019• 4 citations
Publisher

Abstract

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.

DOI
10.1142/s021827182040009x

Related papers

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

C. Stornaiolo

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.

arXiv:1810.04616•International Journal of Geometric Methods in Modern Physics•Oct 31, 2018•4 citations

Emergent classical universes from initial quantum states in a tomographical description

C. Stornaiolo

Quantum and classical physical states are represented in a unified way when they aredescribed by symplectic tomography. Therefore this representation allows us to study directly the necessary conditions for a classical universe to emerge from a quantum state. In a previous work on the de Sitter universe this was done by comparing the classical limit of the quantum tomograms with those resulting from the classical cosmological equations. In this paper, we first review these results and extend them to all the de Sitter models. We show further that these tomograms can be obtained directly from transposing the Wheeler–De Witt equation to the tomographic variables. Subsequently, because the classic limits of the quantum tomograms are identified with their asymptotic expressions, we find the necessary conditions to extend the previous results by taking the tomograms of the WKB solutions of the Wheeler–DeWitt equation with an any potential. Furthermore, in the previous works, we found that the de Sitter models undergo the quantum-to-classical transition when the cosmological constant decays to its present value, we discuss at the end how far we can extend this result to more general models. In the conclusions, after discussing any improvements and developments of the results of this work, we sketch a phenomenological approach from which to extract information about the initial states of the universe.

arXiv:2007.03726•International Journal of Geometric Methods in Modern Physics•Aug 3, 2020•13 citations

Tomography of quantum states of the universe and cosmological dynamics

C. Stornaiolo

It has been proven that conventional quantum mechanics can be reformulated without using the concept of wave function or matrix density. Quantum states can be described in terms of a standard positive probability distribution. Such probability distributions (tomograms) satisfy classical-like equations, which substitute the Schrödinger equation. We consider quantum cosmology in the probability distribution approach. We derive the tomogram corresponding to theWheeler-de Witt equation. We also use the circumstance that cosmological evolution equations for a homogeneous and isotropic universe can be converted into very simple classical equations to derive a quantum cosmological model which links the tomogram reconstructed from observations to the initial conditions of the universe.

Journal of Physics Conference Series•Mar 1, 2006•3 citations

Tomography in Loop Quantum Cosmology

Jasel Berra–Montiel, Alberto Molgado

We analyze the tomographic representation for the Friedmann-Robertson-Walker (FRW) model within the Loop Quantum Cosmology framework. We focus on the Wigner quasi-probability distributions associated with Gaussian and Schrödinger cat states, and then, by applying a Radon integral transform for those Wigner functions, we are able to obtain the symplectic tomograms which define measurable probability distributions that fully characterize the quantum model of our interest. By appropriately introducing the quantum dispersion for a rotated and squeezed quadrature operator in terms of the position and momentum, we efficiently interpret the properties of such tomograms, being consequent with Heisenberg's uncertainty principle. We also obtain, by means of the dual tomographic symbols, the expectation value for the volume operator, which coincides with the values reported in the literature. We expect that our findings result interesting as the introduced tomographic representation may be further benefited from the well-developed measure techniques in the areas of Quantum optics and Quantum information theory.

arXiv:2104.09721•Apr 20, 2021•0 citations

Quantum nondemolition of the Universe

Brian P. Dolan

The role of decohering histories in a quantum description of the Universe is examined. A sufficient condition for different histories to decohere is derived, the cosmological nondemolition condition. This condition automatically ensures that quantum histories decohere regardless of the initial wave function of the Universe.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Oct 15, 1993•0 citations

Quantum-to-classical transition of primordial cosmological perturbations in de Broglie–Bohm quantum theory

Nelson Pinto-Neto, Grasiele Batista dos Santos, Ward Struyve

There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition from quantum to classical fluctuations is plagued with important conceptual issues, most of them related to the application of standard quantum theory to the Universe as a whole. In this paper, we show how these issues can easily be overcome in the framework of the de Broglie--Bohm quantum theory. This theory is an alternative to standard quantum theory that provides an objective description of physical reality, where rather ambiguous notions of measurement or observer play no fundamental role, and which can hence be applied to the Universe as a whole. In addition, it allows for a simple and unambiguous characterization of the classical limit.

arXiv:1110.1339•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Apr 4, 2012•61 citations
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.
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.
Quantum and classical physical states are represented in a unified way when they aredescribed by symplectic tomography. Therefore this representation allows us to study directly the necessary conditions for a classical universe to emerge from a quantum state. In a previous work on the de Sitter universe this was done by comparing the classical limit of the quantum tomograms with those resulting from the classical cosmological equations. In this paper, we first review these results and extend them to all the de Sitter models. We show further that these tomograms can be obtained directly from transposing the Wheeler–De Witt equation to the tomographic variables. Subsequently, because the classic limits of the quantum tomograms are identified with their asymptotic expressions, we find the necessary conditions to extend the previous results by taking the tomograms of the WKB solutions of the Wheeler–DeWitt equation with an any potential. Furthermore, in the previous works, we found that the de Sitter models undergo the quantum-to-classical transition when the cosmological constant decays to its present value, we discuss at the end how far we can extend this result to more general models. In the conclusions, after discussing any improvements and developments of the results of this work, we sketch a phenomenological approach from which to extract information about the initial states of the universe.
It has been proven that conventional quantum mechanics can be reformulated without using the concept of wave function or matrix density. Quantum states can be described in terms of a standard positive probability distribution. Such probability distributions (tomograms) satisfy classical-like equations, which substitute the Schrödinger equation. We consider quantum cosmology in the probability distribution approach. We derive the tomogram corresponding to theWheeler-de Witt equation. We also use the circumstance that cosmological evolution equations for a homogeneous and isotropic universe can be converted into very simple classical equations to derive a quantum cosmological model which links the tomogram reconstructed from observations to the initial conditions of the universe.
We analyze the tomographic representation for the Friedmann-Robertson-Walker (FRW) model within the Loop Quantum Cosmology framework. We focus on the Wigner quasi-probability distributions associated with Gaussian and Schrödinger cat states, and then, by applying a Radon integral transform for those Wigner functions, we are able to obtain the symplectic tomograms which define measurable probability distributions that fully characterize the quantum model of our interest. By appropriately introducing the quantum dispersion for a rotated and squeezed quadrature operator in terms of the position and momentum, we efficiently interpret the properties of such tomograms, being consequent with Heisenberg's uncertainty principle. We also obtain, by means of the dual tomographic symbols, the expectation value for the volume operator, which coincides with the values reported in the literature. We expect that our findings result interesting as the introduced tomographic representation may be further benefited from the well-developed measure techniques in the areas of Quantum optics and Quantum information theory.
There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition from quantum to classical fluctuations is plagued with important conceptual issues, most of them related to the application of standard quantum theory to the Universe as a whole. In this paper, we show how these issues can easily be overcome in the framework of the de Broglie--Bohm quantum theory. This theory is an alternative to standard quantum theory that provides an objective description of physical reality, where rather ambiguous notions of measurement or observer play no fundamental role, and which can hence be applied to the Universe as a whole. In addition, it allows for a simple and unambiguous characterization of the classical limit.