Abstract
Flat space cosmologies (FSCs) are time dependent solutions of three-dimensional (3D) gravity with a vanishing cosmological constant. They can be constructed from a discrete quotient of empty 3D flat spacetime and are also called shifted-boost orbifolds. Using this quotient structure, we build a new and generalized Selberg zeta function for FSCs, and show that it is directly related to the scalar 1-loop partition function. We then propose an extension of this formalism applicable to more general quotient manifolds \( \mathcal{M} \)/ℤ, based on representation theory of fields propagating on this background. Our prescription constitutes a novel and expedient method for calculating regularized 1-loop determinants, without resorting to the heat kernel. We compute quasinormal modes in the FSC using the zeroes of a Selberg zeta function, and match them to known results.
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Acknowledgments
We would like to thank the Niels Bohr Institute for hospitality during the beginning of this collaboration. We thank Daniel Grumiller for comments on the manuscript.
AB is partially supported by a Swarnajayanti Fellowship of the Science and Engineering Research Board (SERB) and also by the following SERB grants SB/SJF/2019-20/08, CRG/2020/002035. CK is supported by the U.S. Department of Energy under grant number DE-SC0019470 and by the Heising-Simons Foundation “Observational Signatures of Quantum Gravity” collaboration grant 2021-2818. VM and RP are supported by the Icelandic Research Fund under grants 195970-053 and 228952-051 and by the University of Iceland Research Fund. VM and RP would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme “Black holes: bridges between number theory and holographic quantum information” when work on this paper was undertaken. This work was supported by: EPSRC Grant number EP/R014604/1.
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Bagchi, A., Keeler, C., Martin, V. et al. A generalized Selberg zeta function for flat space cosmologies. J. High Energ. Phys. 2024, 66 (2024). https://doi.org/10.1007/JHEP04(2024)066
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DOI: https://doi.org/10.1007/JHEP04(2024)066