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    Testing classical-quantum gravity with geodesic deviation

    Tomoya Hirotani*

    Akira Matsumura†

    • Department of Physics, Kyushu University, 744 Motooka, Nishi-Ku, Fukuoka 819-0395, Japan

    • Department of Physics, Kyushu University, 744 Motooka, Nishi-Ku, Fukuoka 819-0395, Japan and Quantum and Spacetime Research Institute, Kyushu University, 744 Motooka, Nishi-Ku, Fukuoka 819-0395, Japan

    • *Contact author: hirotani.tomoya.937@s.kyushu-u.ac.jp
    • †Contact author: matsumura.akira@phys.kyushu-u.ac.jp

    Phys. Rev. D 114, 026014 – Published 8 July, 2026

    DOI: https://doi.org/10.1103/fx1h-97sx

    Abstract

    A novel semiclassical gravity model proposed by Oppenheim et al., that consistently describes interactions between quantum systems and a classical gravitational field, has recently attracted considerable attention. However, the limitations and phenomenological viability of this model have not yet been thoroughly investigated. In this work, based on the model, we study quantum fluctuations of geodesic deviation coupled with a classical gravitational field. We analytically derive the strain spectrum expected from the fluctuations and show that the original Oppenheim et al. model can be tested with the current observational sensitivity of gravitational-wave experiments. Furthermore, motivated by the novel semiclassical model, we construct two additional models; a modified Oppenheim et al. model that is manifestly consistent with Bianchi identities, and a classical-quantum model with environment-induced noise. We analyze the strain spectra predicted by these two models through comparison with those of the original Oppenheim et al. model and perturbative quantum gravity.

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