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Next-generation ground-based gravitational-wave observatories such as theEinstein Telescope and Cosmic Explorer will detect $O(10^{5}-10^{6})$ signalsfrom compact binary coalescences every year, the exact number depending onuncertainties in the binary merger rate. Several overlapping signals will bepresent in band at any given time, generating a confusion noise background. Westudy how this confusion noise affects constraints on possible deviations fromgeneral relativity induced by modified gravity and environmental effects.Confusion noise impacts only the signals that last longer in band. Even for a"golden" GW170817-like signal, the constraints broaden by a factor in the range$[10\%,40\%]$ $([70\%,110\%])$ for the fiducial (highest) value of the localbinary neutron star merger rate. Our ability to test general relativity orconstrain environmental effects will be limited by systematic errors, and notby confusion noise.

The impact of compact binary confusion noise on tests of fundamental physics with next-generation gravitational-wave detectors