模拟标量Galileons的适定性UV完备化
A Well-Posed UV Completion for Simulating Scalar Galileons
摘要：
伽利略标量场理论是有效场论的一个典型例子，它展示了万施泰因屏蔽机制，这被纳入了爱因斯坦引力的许多扩展。伽利略号描述了引力辐射的螺旋度为零的模式，它的存在对轨道物体的引力波的预测以及对引力对附加偏振敏感的测试有重要意义。由于它们相互作用的衍生性质，表面上伽利略子并不适合作为有效场论。虽然这种性质被恰当地理解为仅仅是有效场论截断的一个伪像，并且在理论上并不令人担忧，但是在实际水平上，它仍然使数值模拟非常成问题。尽管如此，以前的数值方法已经成功地发展了合理的初始数据的系统，慢慢打开的相互作用。在这里，我们提出了两种替代方法来提高数值稳定性Galileon数值模拟。其中之一是对以前的方法进行了微小的修改，该方法引入了一个低通滤波器，相当于施加UV截止以及打开相互作用的松弛方法。第二种方法相当于构建一个（数值）UV完成，其中高动量模式的动力学受到控制，并且不需要慢慢打开非线性相互作用。我们表明，数值模拟的UV理论成功地再现正确的Galileon动力学在低能量，低通滤波器的方法和以前的数值模拟一致。
英文摘要：
The Galileon scalar field theory is a prototypical example of an effective field theory that exhibits the Vainshtein screening mechanism, which is incorporated into many extensions to Einstein gravity. The Galileon describes the helicity zero mode of gravitational radiation, the presence of which has significant implications for predictions of gravitational waves from orbiting objects, and for tests of gravity sensitive to additional polarizations. Because of the derivative nature of their interactions, Galileons are superficially not well-posed as effective field theories. Although this property is properly understood merely as an artifact of the effective field theory truncation, and is not theoretically worrisome, at the practical level it nevertheless renders numerical simulation highly problematic. Notwithstanding, previous numerical approaches have successfully evolved the system for reasonable initial data by slowly turning on the interactions. We present here two alternative approaches to improving numerical stability in Galileon numerical simulations. One of these is a minor modification of previous approaches, which introduces a low pass filter that amounts to imposing a UV cutoff together with a relaxation method of turning on interactions. The second approach amounts to constructing a (numerical) UV completion for which the dynamics of the high momentum modes is under control, and for which it is unnecessary to slowly turn on nonlinear interactions. We show that numerical simulations of the UV theory successfully reproduce the correct Galileon dynamics at low energies, consistent with the low-pass filter method and with previous numerical simulations.
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