Evolution of confined quantum scalar fields in curved spacetime. Part I: Spacetimes without boundaries or with static boundaries in a synchronous gauge

We develop a method for computing the Bogoliubov transformation experienced by a confined quantum scalar field in a globally hyperbolic spacetime, due to the changes in the geometry and/or the confining boundaries. The method constructs a basis of modes of the field associated to each Cauchy hypersurface, by means of an eigenvalue problem posed in the hypersurface. The Bogoliubov transformation between bases associated to different times can be computed through a differential equation, which coefficients have simple expressions in terms of the solutions to the eigenvalue problem. This transformation can be interpreted physically when it connects two regions of the spacetime where the metric is static. Conceptually, the method is a generalisation of Parker’s early work on cosmological particle creation. It proves especially useful in the regime of small perturbations, where it allows one to easily make quantitative predictions on the amplitude of the resonances of the field, providing an important tool in the growing research area of confined quantum fields in table-top experiments. We give examples within the perturbative regime (gravitational waves) and the non-perturbative regime (cosmological particle creation). This is the first of two articles introducing the method, dedicated to spacetimes without boundaries or which boundaries remain static in some synchronous gauge.

10.1140/epjc/s10052-020-8369-9

1434-6044

Barbado, Luis C.

50e4b0e1-c3a7-4aa8-8306-522285b64207

Báez-Camargo, Ana L.

a179fdc4-7678-4bd6-9674-7fe3d3a0eb4f

Fuentes, Ivette

c6d65a4c-feac-44c1-9097-e0f6a9e0cf44

1 August 2020

Barbado, Luis C.

50e4b0e1-c3a7-4aa8-8306-522285b64207

Báez-Camargo, Ana L.

a179fdc4-7678-4bd6-9674-7fe3d3a0eb4f

Fuentes, Ivette

c6d65a4c-feac-44c1-9097-e0f6a9e0cf44

Barbado, Luis C., Báez-Camargo, Ana L. and Fuentes, Ivette (2020) Evolution of confined quantum scalar fields in curved spacetime. Part I: Spacetimes without boundaries or with static boundaries in a synchronous gauge. European Physical Journal C, 80 (8), [796]. (doi:10.1140/epjc/s10052-020-8369-9).

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Published date: 1 August 2020

Additional Information: Funding Information: The authors especially want to thank Jorma Louko for the rich exchange of ideas with us, which greatly helped solving many issues and significantly improved the article. We also want to thank Eugenia Colafranceschi, David E. Bruschi, Tupac Bravo, Daniel Hartley, Maximilian P. E. Lock, Richard Howl, Joel Lindkvist, Jan Kohlrus, Dennis Rätzel, Carlos Barceló and Stephan Huimann for their useful comments and discussions during the elaboration of this article. We are equally grateful to Miguel Sánchez Caja, Felix Finster and Simone Murro for clarifying our doubts on the mathematical background. Finally, we would like to thank an anonymous referee for some useful comments which helped to clarify the details of our mathematical construction. L. C. B. acknowledges the support from the research platform TURIS and from the European Commission via Testing the Large-Scale Limit of Quantum Mechanics (TEQ) (No. 766900) project, and from the Austrian-Serbian bilateral scientific cooperation no. 451-03-02141/2017-09/02. A. L. B. recognises support from CONACyT ref:579920/410674. I. F. would like to acknowledge that this project was made possible through the support of the Penrose Institute, the grant “Quantum Observers in a Relativistic World” from FQXi’s Physics of the Observer program, and the grant “Leaps in cosmology: gravitational wave detection with quantum systems” (No. 58745) from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. Funding Information: The authors especially want to thank Jorma Louko for the rich exchange of ideas with us, which greatly helped solving many issues and significantly improved the article. We also want to thank Eugenia Colafranceschi, David E. Bruschi, Tupac Bravo, Daniel Hartley, Maximilian P.?E. Lock, Richard Howl, Joel Lindkvist, Jan Kohlrus, Dennis R?tzel, Carlos Barcel? and Stephan Huimann for their useful comments and discussions during the elaboration of this article. We are equally grateful to Miguel S?nchez Caja, Felix Finster and Simone Murro for clarifying our doubts on the mathematical background. Finally, we would like to thank an anonymous referee for some useful comments which helped to clarify the details of our mathematical construction. L.?C.?B. acknowledges the support from the research platform TURIS and from the European Commission via Testing the Large-Scale Limit of Quantum Mechanics (TEQ) (No.?766900) project, and from the Austrian-Serbian bilateral scientific cooperation no. 451-03-02141/2017-09/02. A.?L.?B. recognises support from CONACyT ref:579920/410674. I.?F. would like to acknowledge that this project was made possible through the support of the Penrose Institute, the grant ?Quantum Observers in a Relativistic World? from FQXi?s Physics of the Observer program, and the grant ?Leaps in cosmology: gravitational wave detection with quantum systems? (No.?58745) from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. Publisher Copyright: © 2020, The Author(s).