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One approach to testing general relativity (GR) introduces free parameters inthe post-Newtonian (PN) expansion of the gravitational-wave (GW) phase. Ifsystematic errors on these testing GR (TGR) parameters exceed the statisticalerrors, this may signal a false violation of GR. Here, we consider systematicerrors produced by unmodeled binary eccentricity. Since the eccentricity of GWevents in ground-based detectors is expected to be small or negligible, the useof quasicircular waveform models for testing GR may be safe when analyzing asmall number of events. However, as the catalog size of GW detectionsincreases, more stringent bounds on GR deviations can be placed by combininginformation from multiple events. In that case, even small systematic biasesmay become significant. We apply the approach of hierarchical Bayesianinference to model the posterior probability distributions of the TGRparameters inferred from a population of eccentric binary black holes (BBHs).We assume each TGR parameter value varies across the BBH population accordingto a Gaussian distribution. We compute the posterior distributions for theseGaussian hyperparameters. This is done for LIGO and Cosmic Explorer (CE). Wefind that systematic biases from unmodeled eccentricity can signal false GRviolations for both detectors when considering constraints set by a catalog ofevents. We also compute the projected bounds on the $10$ TGR parameters wheneccentricity is included as a parameter in the waveform model. We find that thefirst four dimensionless TGR deformation parameters can be bounded at $90\%$confidence to $\delta \hat{\varphi}_i \lesssim 10^{-2}$ for LIGO and $\lesssim10^{-3}$ for CE [where $i=(0,1,2,3)$]. In comparison to the circular orbitcase, the combined bounds on the TGR parameters worsen by a modest factor of$\lesssim 2$ when eccentricity is included in the waveform.

Eccentricity-induced systematic error on parametrized tests of general  relativity: hierarchical Bayesian inference applied to a binary black hole  population