Unattainability of the trans-Planckian regime in nonlocal quantum gravity
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Springer
Received: March 20, Revised: August 13, Accepted: August 14, Published: September 7,
2020 2020 2020 2020
F. Briscesea,b,1 and L. Modestoc a
Academy for Advanced Interdisciplinary Studies, Southern University of Science and Technology, Shenzhen 518055, China b INdAM, Citt` a Universitaria, P.le A. Moro 5, 00185 Rome, Italy c Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
E-mail: [email protected], [email protected] Abstract: Based on the ultraviolet asymptotic freedom of nonlocal quantum gravity, we show that the trans-Planckian energy regime is unattainable in laboratory experiments. As physical implications, it turns out that the violation of causality, typical of nonlocal field theories, can never be detected in particle accelerators, while the asymptotic freedom of the theory provides an elegant solution to the so called trans-Planckian cosmological problem. Keywords: Cosmology of Theories beyond the SM, Models of Quantum Gravity ArXiv ePrint: 1912.01878
1
Corresponding author.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)056
JHEP09(2020)056
Unattainability of the trans-Planckian regime in nonlocal quantum gravity
Contents 1 Introduction
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2 Ultraviolet asymptotic freedom of nonlocal quantum gravity
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3 Unattainability of the trans-Planckian regime and undetectability of causality violations
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5 Conclusions
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Introduction
The idea that a renormalizable quantum theory of gravitation can be achieved by introducing higher derivatives or nonlocal interactions was suggested long time ago by Stelle [1, 2], Krasnikov [3], and Kuz’min [4]. This proposal for an ultraviolet completion of EinsteinHilbert (EH) gravity was subsequently abandoned, since the specific models studied in [1– 4] contain ineradicable ghosts. However, nonlocal models have been revisited in recent years [5–11], when it became clear that, under certain conditions that restrict the type of nonlocality, it is possible to avoid ghosts. In facts, it has been shown that the complex scattering amplitudes in nonlocal field theories satisfy the Cutkosky rules [12–15], so that the unitarity is preserved at any pertutbative order in the loop expansion. We mention that higher derivatives and Lee-Wick quantum gravity are also under current investigation, see [16–25]. In particular, Lee-Wick theory has extra complex conjugate poles corresponding to ghosts, that can be consistently removed from the physical spectrum and never go on shell [21–24]; see also [25] for a discussion of ghost-related issues in fourth-order quantum gravity. Therefore, in order to achieve a renormalizable quantum theory of gravitational interactions, one is forced to introduce a new nonlocal or higher derivative action principle. In this paper we will focus on nonlocal quantum gravity [5–11], but most of the results reported here are still valid for other higher-derivative theories [16–25]. Nonlocal quantum gravity is well defined at classical as well as
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