Abstract
In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA,we present here a sample of what we view as particularly promising fundamental physics directions. We organize these directions through a “science-first” approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics.

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Notes
The term charge is used here loosely, to refer to a non-trivial configuration of some new field, as has become customary in the relevant literature.
Technically speaking, the non-minimal coupling in the action is through the product of a pseudoscalar and the Pontryagin density and the action is parity invariant. The solutions exhibit parity violations.
The well-motivated assumption that black holes should be uncharged could also be tested; see [93] for work in this direction.
IMBHBs will also be detected at cosmological distances, but their existence is still debated nowadays and consequently no cosmological applications of this class of sources have ever been considered.
A correction of N post-Newtonian, or NPN, order is one that is of \({{\mathcal {O}}}(v^{2N}/c^{2N})\) relative to the GR leading order term [249].
The original ppE formalism also proposes a similar way to parameterize non-GR modifications in the ringdown phase [246].
A term that scales as \((v/c)^{2N}\) is said to be of N PN order relative to its leading-order controlling factor.
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Acknowledgements
We would like to thank all of the attendees of the first, inaugural meeting of the Fundamental Physics Research Group in Florence for interesting and stimulating discussions and presentations. We would also like to thank the Galileo Galilei Institute for their hospitality during the organization of this meeting. E. Barausse, A. Dima, N. Franchini and S. Völkel acknowledge financial support provided under the European Union’s H2020 ERC Consolidator Grant “GRavity from Astrophysical to Microscopic Scales” Grant agreement No. GRAMS-815673. This work has also been supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant agreement No. 690904. The authors would like to acknowledge financial and networking support by the GWverse COST Action CA16104, “Black holes, gravitational waves and fundamental physics”; the European Research Council Starting Grant DarkGRA-757480 (“Unveiling the dark universe with gravitational waves”) and the Flemish Research Council through the Odysseus Grant G.0011.12. H. Witek acknowledges financial support provided by the Royal Society University Research Fellowship UF160547 and the Royal Society Research Grant RGF\(\backslash \)R1\(\backslash \)180073. S.A. Hughes’s work on LISA-related science is supported by NASA Grant No. 80NSSC18K1091. E. Berti is supported by NSF Grants No. PHY-1912550 and AST-1841358, NASA ATP Grants No. 17-ATP17-0225 and 19-ATP19-0051, and NSF-XSEDE Grant No. PHY-090003. N.Yunes acknowledges support from NSF grant PHY-1759615, and NASA Grants 80NSSC18K1352. K. Yagi acknowledges support from NSF Award PHY-1806776, a Sloan Foundation Research Fellowship, and the Ed Owens Fund. T. P. Sotiriou acknowledges partial support from the STFC Consolidated Grant No. ST/P000703/1.
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Barausse, E., Berti, E., Hertog, T. et al. Prospects for fundamental physics with LISA. Gen Relativ Gravit 52, 81 (2020). https://doi.org/10.1007/s10714-020-02691-1
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DOI: https://doi.org/10.1007/s10714-020-02691-1