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Evolution of the Quantum Friedmann Universe Featuring Radiation
General Relativity and Quantum Cosmology · Submitted 7 Feb 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It has been shown that, under certain conditions, the quantum universe can be in quasistationary states.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
The classical and quantum models of the Friedmann universe originally filled with a scalar field and radiation have been studied. The radiation has been used to specify a reference frame that makes it possible to remove ambiguities in choosing the time coordinate. Solutions to the Einstein and Schroedinger equations have been studied under the assumption that the rate of scalar-field variation is much less than the rate of universe expansion (contraction). It has been shown that, under certain conditions, the quantum universe can be in quasistationary states. The probability that the universe goes over to states with large quantum numbers owing to the interaction of the scalar and gravitational fields is nonzero. It has been shown that, in the lowest state, the scale factor is on order of the Planck length. The matter- and radiation-energy densities in the Planck era have been computed. The possible scenarios of Universe evolution are discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The classical and quantum models of the Friedmann universe originally filled with a scalar field and radiation have been studied. | contribution 0.77 | 0.64 | 0.04 | asserted 0.95 |
| s1 | The radiation has been used to specify a reference frame that makes it possible to remove ambiguities in choosing the time coordinate. | method 0.95 | 0.67 | 0.04 | asserted 1.00 |
| s2 | Solutions to the Einstein and Schroedinger equations have been studied under the assumption that the rate of scalar-field variation is much less than the rate of universe expansion (contraction). | method 0.87 | 0.83 | 0.04 | asserted 0.88 |
| s3 | It has been shown that, under certain conditions, the quantum universe can be in quasistationary states. | result 1.00 | 0.88 | 0.28 | asserted 0.95 |
| s4 | The probability that the universe goes over to states with large quantum numbers owing to the interaction of the scalar and gravitational fields is nonzero. | result 1.00 | 0.84 | 0.19 | asserted 0.93 |
| s5 | It has been shown that, in the lowest state, the scale factor is on order of the Planck length. | result 1.00 | 0.89 | 0.18 | asserted 1.00 |
| s6 | The matter- and radiation-energy densities in the Planck era have been computed. | result 0.93 | 0.90 | 0.07 | asserted 1.00 |
| s7 | The possible scenarios of Universe evolution are discussed. | interpretation 0.52 | 0.71 | 0.07 | unclear 0.52 |
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Original abstract
The classical and quantum models of the Friedmann universe originally filled with a scalar field and radiation have been studied. The radiation has been used to specify a reference frame that makes it possible to remove ambiguities in choosing the time coordinate. Solutions to the Einstein and Schroedinger equations have been studied under the assumption that the rate of scalar-field variation is much less than the rate of universe expansion (contraction). It has been shown that, under certain conditions, the quantum universe can be in quasistationary states. The probability that the universe goes over to states with large quantum numbers owing to the interaction of the scalar and gravitational fields is nonzero. It has been shown that, in the lowest state, the scale factor is on order of the Planck length. The matter- and radiation-energy densities in the Planck era have been computed. The possible scenarios of Universe evolution are discussed.
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