Weakly-coupled stealth solution in scordatura degenerate theory
Weakly-coupled stealth solution in scordatura degenerate theory
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DOI：
10.1088/1475-7516/2020/01/030
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发表时间：
2019-12
影响因子：
6.4
通讯作者：
H. Motohashi;S. Mukohyama
中科院分区：
文献类型：
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作者：
H. Motohashi;S. Mukohyama
在标量-张量理论中，我们重新讨论了隐形解周围扰动的强耦合问题，即背景具有与广义相对论中相同的度量形式，但具有标量场的非平凡配置。其中最简单的是隐形闵可夫斯基（或德西特）解决方案与常数，类时衍生的标量场，即鬼凝聚。在解耦极限下，描述隐形闵可夫斯基（或德西特）解周围扰动的有效场论（EFT）显示出形式为ω2 = α k4/M2的普遍色散关系，其中M是表征背景标量场的质量尺度，α是无量纲常数。假设α是正的并且阶数为1，一个简单的标度论证表明EFT一直弱耦合到M。另一方面，如果基础理论的结构迫使微扰遵循二阶运动方程，那么α=0，色散关系不再依赖于空间动量。这不仅解释了最近在一类简并理论中指出的强耦合问题的起源，而且为该问题的可能解决方案提供了线索。然后，我们认为，一个控制失谐的退化条件，我们称之为scordatura，呈现弱耦合的扰动，而不改变在天体物理尺度的退化理论的隐形解决方案的属性。
In scalar-tensor theories we revisit the issue of strong coupling of perturbations around stealth solutions, i.e. backgrounds with the same forms of the metric as in General Relativity but with non-trivial configurations of the scalar field. The simplest among them is a stealth Minkowski (or de Sitter) solution with a constant, timelike derivative of the scalar field, i.e. ghost condensation. In the decoupling limit the effective field theory (EFT) describing perturbations around the stealth Minkowski (or de Sitter) solution shows the universal dispersion relation of the form ω2 = α k4/M2, where M is a mass scale characterizing the background scalar field and α is a dimensionless constant. Provided that α is positive and of order unity, a simple scaling argument shows that the EFT is weakly coupled all the way up to M. On the other hand, if the structure of the underlining theory forces the perturbations to follow second-order equations of motion then α=0 and the dispersion relation loses dependence on the spatial momentum. This not only explains the origin of the strong coupling problem that was recently pointed out in a class of degenerate theories but also provides a hint for a possible solution of the problem. We then argue that a controlled detuning of the degeneracy condition, which we call scordatura, renders the perturbations weakly coupled without changing the properties of the stealth solutions of degenerate theories at astrophysical scales.