Tests of general relativity using analytic derivatives of parametrized post-Einsteinian gravitational waveforms within the Fisher-matrix framework
Abstract
Testing gravity beyond general relativity (GR) is essential for probing fundamental physics in the strong-field and highly dynamical regime accessed by gravitational-wave (GW) observations. In this work, we derive analytic expressions for waveform derivatives in the Fisher-matrix formalism within the parametrized post-Einsteinian framework, using the frequency-domain inspiral waveform. These analytic derivatives enable stable and efficient Fisher-matrix calculations without relying on finite-difference schemes. We apply this method to a wide range of detector configurations, including space-based, ground-based, and multiband observations, and combine it with different binary black hole population models. Our results reveal clear and systematic trends in the constraints on non-GR effects as functions of post-Newtonian order, detector type, and source population. They also demonstrate the complementarity between space- and ground-based detectors, particularly for effects that accumulate during the low-frequency inspiral. The analytic approach substantially reduces computational cost and avoids numerical systematics associated with step-size choices, making it well suited for large-scale parameter studies. These results provide robust forecasts for the capability of future GW observations to constrain a broad class of non-GR effects and environmental influences, highlighting the scientific potential of upcoming detector networks for precision tests of gravity.
Versions
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BibTeX
@misc{wu2026tests,
title = {{Tests of general relativity using analytic derivatives of parametrized post-Einsteinian gravitational waveforms within the Fisher-matrix framework}},
author = {Jie Wu and Mengfei Sun and Jin Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.04238},
eprint = {2607.04238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04238},
}
RIS
TY - UNPB
TI - Tests of general relativity using analytic derivatives of parametrized post-Einsteinian gravitational waveforms within the Fisher-matrix framework
AU - Jie Wu
AU - Mengfei Sun
AU - Jin Li
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2607.04238
UR - https://arxiv.org/abs/2607.04238
AB - Testing gravity beyond general relativity (GR) is essential for probing fundamental physics in the strong-field and highly dynamical regime accessed by gravitational-wave (GW) observations. In this work, we derive analytic expressions for waveform derivatives in the Fisher-matrix formalism within the parametrized post-Einsteinian framework, using the frequency-domain inspiral waveform. These analytic derivatives enable stable and efficient Fisher-matrix calculations without relying on finite-difference schemes. We apply this method to a wide range of detector configurations, including space-based, ground-based, and multiband observations, and combine it with different binary black hole population models. Our results reveal clear and systematic trends in the constraints on non-GR effects as functions of post-Newtonian order, detector type, and source population. They also demonstrate the complementarity between space- and ground-based detectors, particularly for effects that accumulate during the low-frequency inspiral. The analytic approach substantially reduces computational cost and avoids numerical systematics associated with step-size choices, making it well suited for large-scale parameter studies. These results provide robust forecasts for the capability of future GW observations to constrain a broad class of non-GR effects and environmental influences, highlighting the scientific potential of upcoming detector networks for precision tests of gravity.
ER -