Von Neumann algebra description of inflationary cosmology
Abstract We study the von Neumann algebra description of the inflationary quasi-de Sitter (dS) space. Unlike perfect dS space, quasi-dS space allows the nonzero energy flux across the horizon, which can be identified with the expectation value of the static time translation generator. Moreover, as a...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-11-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-12202-6 |
| _version_ | 1827300975438725120 |
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| author | Min-Seok Seo |
| author_facet | Min-Seok Seo |
| author_sort | Min-Seok Seo |
| collection | DOAJ |
| description | Abstract We study the von Neumann algebra description of the inflationary quasi-de Sitter (dS) space. Unlike perfect dS space, quasi-dS space allows the nonzero energy flux across the horizon, which can be identified with the expectation value of the static time translation generator. Moreover, as a dS isometry associated with the static time translation is spontaneously broken, the fluctuation in time is accumulated, which induces the fluctuation in the energy flux. When the inflationary period is given by $$(\epsilon _H H)^{-1}$$ ( ϵ H H ) - 1 where $$\epsilon _H$$ ϵ H is the slow-roll parameter measuring the increasing rate of the Hubble radius, both the energy flux and its fluctuation diverge in the $$G \rightarrow 0$$ G → 0 limit. Taking the fluctuation in the energy flux and that in the observer’s energy into account, we argue that the inflationary quasi-dS space is described by Type II $$_\infty $$ ∞ algebra. As the entropy is not bounded from above, this is different from Type II $$_1$$ 1 description of perfect dS space in which the entropy is maximized by the maximal entanglement. We also show that our result is consistent with the observation that the von Neumann entropy for the density matrix reflecting the fluctuations above is interpreted as the generalized entropy. |
| first_indexed | 2024-03-11T11:00:54Z |
| format | Article |
| id | doaj.art-29ce143320b242dc88f01cbe9eae2edc |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-24T16:14:05Z |
| publishDate | 2023-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-29ce143320b242dc88f01cbe9eae2edc2024-03-31T11:30:35ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-11-01831111410.1140/epjc/s10052-023-12202-6Von Neumann algebra description of inflationary cosmologyMin-Seok Seo0Department of Physics Education, Korea National University of EducationAbstract We study the von Neumann algebra description of the inflationary quasi-de Sitter (dS) space. Unlike perfect dS space, quasi-dS space allows the nonzero energy flux across the horizon, which can be identified with the expectation value of the static time translation generator. Moreover, as a dS isometry associated with the static time translation is spontaneously broken, the fluctuation in time is accumulated, which induces the fluctuation in the energy flux. When the inflationary period is given by $$(\epsilon _H H)^{-1}$$ ( ϵ H H ) - 1 where $$\epsilon _H$$ ϵ H is the slow-roll parameter measuring the increasing rate of the Hubble radius, both the energy flux and its fluctuation diverge in the $$G \rightarrow 0$$ G → 0 limit. Taking the fluctuation in the energy flux and that in the observer’s energy into account, we argue that the inflationary quasi-dS space is described by Type II $$_\infty $$ ∞ algebra. As the entropy is not bounded from above, this is different from Type II $$_1$$ 1 description of perfect dS space in which the entropy is maximized by the maximal entanglement. We also show that our result is consistent with the observation that the von Neumann entropy for the density matrix reflecting the fluctuations above is interpreted as the generalized entropy.https://doi.org/10.1140/epjc/s10052-023-12202-6 |
| spellingShingle | Min-Seok Seo Von Neumann algebra description of inflationary cosmology European Physical Journal C: Particles and Fields |
| title | Von Neumann algebra description of inflationary cosmology |
| title_full | Von Neumann algebra description of inflationary cosmology |
| title_fullStr | Von Neumann algebra description of inflationary cosmology |
| title_full_unstemmed | Von Neumann algebra description of inflationary cosmology |
| title_short | Von Neumann algebra description of inflationary cosmology |
| title_sort | von neumann algebra description of inflationary cosmology |
| url | https://doi.org/10.1140/epjc/s10052-023-12202-6 |
| work_keys_str_mv | AT minseokseo vonneumannalgebradescriptionofinflationarycosmology |