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 TMF, 2017, Volume 190, Number 3, Pages 533–547 (Mi tmf9121)

Properties of the false vacuum as a quantum unstable state

K. Urbanovski

Institute of Physics, University of Zielona Góra, Zielona Góra, Poland

Abstract: We analyze properties of unstable vacuum states from the standpoint of quantum theory. Some suggestions can be found in the literature that some false (unstable) vacuum states can survive up to times when their survival probability takes a nonexponential form. At asymptotically large times, the survival probability as a function of the time $t$ has an inverse power-law form. We show that in this time region, the energy of false vacuum states tends to the energy of the true vacuum state as $1/t^2$ as $t\to\infty$. This means that the energy density in the unstable vacuum state and hence also the cosmological constant $\Lambda=\Lambda(t)$ should have analogous properties. The conclusion is that $\Lambda$ in a universe with an unstable vacuum should have the form of a sum of the "bare" cosmological constant and a term of the type $1/t^2$: $\Lambda(t)\equiv \Lambda_{bare}+d/t^2$ (where $\Lambda_{bare}$ is the cosmological constant for a universe with the true vacuum).

Keywords: false vacuum, unstable state, cosmological constant

 Funding Agency Grant Number National Science Centre (Narodowe Centrum Nauki) DEC-2013/09/B/ST2/03455 This research was supported in part by the National Science Centre, Poland (Grant No. DEC-2013/09/B/ST2/03455).

DOI: https://doi.org/10.4213/tmf9121

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English version:
Theoretical and Mathematical Physics, 2017, 190:3, 458–469

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Revised: 25.04.2016

Citation: K. Urbanovski, “Properties of the false vacuum as a quantum unstable state”, TMF, 190:3 (2017), 533–547; Theoret. and Math. Phys., 190:3 (2017), 458–469

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf9121
• https://doi.org/10.4213/tmf9121
• http://mi.mathnet.ru/eng/tmf/v190/i3/p533

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Szydlowski M., Stachowski A., Urbanowski K., “Quantum Mechanical Look At the Radioactive-Like Decay of Metastable Dark Energy”, Eur. Phys. J. C, 77:12 (2017), 902
2. Bentivegna E., Branchina V., Contino F., Zappala D., “Impact of New Physics on the Ew Vacuum Stability in a Curved Spacetime Background”, J. High Energy Phys., 2017, no. 12, 100
3. Khurshudyan M., Khurshudyan A., “Phenomenological Modification of Horizon Temperature”, Mod. Phys. Lett. A, 32:29 (2017), 1750156
4. Urbanowski K., “Non-Classical Behavior of Moving Relativistic Unstable Particles”, Acta Phys. Pol. B, 48:8 (2017), 1411–1432
5. Szydlowski M., Stachowski A., Urbanowski K., “Cosmological Implications of Quantum Mechanics Parametrization of Dark Energy”, 8Th International Workshop Dice2016: Spacetime - Matter - Quantum Mechanics, Journal of Physics Conference Series, 880, IOP Publishing Ltd, 2017, 012022
6. Stachowski A., Szydlowski M., Urbanowski K., “Cosmological Implications of the Transition From the False Vacuum to the True Vacuum State”, Eur. Phys. J. C, 77:6 (2017), 357
7. V. Branchina, F. Contino, A. Pilaftsis, “Protecting the stability of the electroweak vacuum from Planck-scale gravitational effects”, Phys. Rev. D, 98:7 (2018), 075001
8. M. Khurshudyan, M. Hakobyan, A. Khurshudyan, “Nonlinear logarithmic interactions and a varying polytropic gas”, Mod. Phys. Lett. A, 33:33 (2018), 1850189
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