Gravitational waves allow us to test general relativity in the highly dynamical regime. While current observations have been consistent with waves emitted by quasi-circular binaries, eccentric binaries may also produce detectable signals in the near future with ground- and space-based detectors. We here explore how tests of general relativity scale with the orbital eccentricity of the source during the inspiral of compact objects up to $e \sim 0.8$. We use a new, 3rd post-Newtonian-accurate, eccentric waveform model for the inspiral of compact objects, which is fast enough for Bayesian parameter estimation and model selection, and highly accurate for modeling moderately eccentric inspirals. We derive and incorporate the eccentric corrections to this model induced in Brans-Dicke theory and in Einstein-dilaton-Gauss-Bonnet gravity at leading post-Newtonian order, which suggest a straightforward eccentric extension of the parameterized post-Einsteinian formalism. We explore the upper limits that could be set on the coupling parameters of these modified theories through both a confidence-interval- and Bayes-factor-based approach, using a Markov-Chain Monte Carlo and a trans-dimensional, reversible-jump, Markov-Chain Monte Carlo method. We find projected constraints with signals from sources with $e \sim 0.4$ that are one order of magnitude stronger than that those obtained with quasi-circular binaries in advanced LIGO. In particular, eccentric gravitational waves detected at design sensitivity should be able to constrain the Brans-Dicke coupling parameter $\omega \gtrsim 3300$ and the Gauss-Bonnet coupling parameter $\alpha^{1/2} \lesssim 0.5 \; {\rm{km}}$ at 90% confidence. Although the projected constraint on $\omega$ is weaker than other current constraints, the projected constraint on $\alpha^{1/2}$ is 10 times stronger than the current gravitational wave bound.

中文翻译：

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用偏心引力波约束引力：投影上限和模型选择

引力波使我们能够在高动态范围内测试广义相对论。虽然目前的观测与准圆形双星发射的波一致，但偏心双星也可能在不久的将来用地面和空间探测器产生可探测的信号。我们在这里探索了在致密物体的吸气过程中，广义相对论的测试如何与源的轨道偏心率成比例地达到 $e \sim 0.8$。我们使用一种新的、第三次后牛顿精确、偏心波形模型用于紧凑物体的螺旋，这对于贝叶斯参数估计和模型选择来说足够快，并且对于模拟适度偏心的螺旋具有很高的准确性。我们导出并合并了对这个模型的偏心校正，这些偏心校正是在 Brans-Dicke 理论和爱因斯坦-扩张-高斯-博内引力在领先的后牛顿阶数中引起的，这表明参数化后爱因斯坦形式主义的直接偏心扩展。我们通过基于置信区间和贝叶斯因子的方法，使用马尔可夫链蒙特卡罗和跨维可逆跳跃马尔可夫，探索可以对这些修正理论的耦合参数设置的上限-链蒙特卡罗方法。我们发现来自具有 $e \sim 0.4$ 的源信号的投影约束比在高级 LIGO 中使用准圆形双星获得的信号强一个数量级。特别是，以设计灵敏度检测到的偏心引力波应该能够约束 Brans-Dicke 耦合参数 $\omega \gtrsim 3300$ 和 Gauss-Bonnet 耦合参数 $\alpha^{1/2} \lesssim 0.5 \；{\rm{km}}$ 置信度为 90%。尽管 $\omega$ 上的投影约束比其他当前约束弱，但 $\alpha^{1/2}$ 上的投影约束比当前引力波边界强 10 倍。