When can we ignore eccentricity when testing general relativity with gravitational waves?

Detections of gravitational waves (GW) emitted from binary black hole (BBH) coalescences allow us to probe the strong-field dynamics of general relativity (GR). One can compare the observed GW signals with theoretical waveform models to constrain possible deviations from GR. Any physics that is not included in these waveform models might show up as apparent GR deviations. The waveform models used in current tests of GR describe binaries on quasicircular orbits, since most of the binaries detected by ground-based gravitational wave detectors are expected to have negligible eccentricities. Thus, a signal from an eccentric binary in GR is likely to show up as a deviation from GR in the current implementation of these tests. We study the response of four standard tests of GR to numerically simulated eccentric BBH signals in the LIGO-Virgo network. Specifically, we consider a test for the consistency between the low- and high-frequency parts of the signal; two tests that introduce parameterized modifications to the phase of the signal (e.g., in the post-Newtonian coefficients); and a test for dispersive propagation effects. We find that signals having larger eccentricities (~0.1) when entering the detector's sensitive band lead to very significant false GR deviations in most tests for the high-SNR cases we consider, while signals having smaller eccentricities (~0.05) still lead to significant deviations in some tests. Thus, it will be necessary to exclude the possibility of an eccentric binary in order to make any claim about detecting a deviation from GR.