级联DGP模型中的临界张力
The critical tension in the Cascading DGP model
摘要：
我们使用基于体块的方法研究了6维级联DGP模型中弱引力场的行为。为了解决余维大于1的膜的薄极限的模糊性，我们考虑了膜的内部结构的一个特定的正则化，其中5D膜可以被认为是相对于4D膜薄。我们考虑了四维膜上纯张力源的解，并研究了这些背景解周围的一阶扰动。我们采用四维标量-矢量-张量分解，并专注于标量部门的扰动。我们表明，在一个合适的四维极限，跟踪部分的四维度规扰动服从解耦方程，这表明它是一个鬼的背景张力小于临界张力，而它是一个健康的领域，否则。我们给出了临界张力存在的几何解释，以及相关场是鬼场还是鬼场取决于背景张力的原因。然而，我们发现一个价值的关键紧张这是不同的一个已经发现在文献中。与文献中的结果相一致，我们的分析表明，适当地选择背景张力，我们可以对理论的自由参数的任何值构造无鬼模型。我们认为，不同之处在于用于评估的余维2膜上的pillbox集成的程序。我们确认我们的分析的有效性，通过在一个特定的情况下，厚COD-2膜内的解决方案是已知的数值积分。我们强调，奇异结构的扰动场的套膜设置是非常微妙的，非常小心时，必须采取推导余维2结的条件。
英文摘要：
We study the behaviour of weak gravitational fields in the 6D Cascading DGP model using a bulk-based approach. To deal with the ambiguity in the thin limit of branes of codimension higher than one, we consider a specific regularization of the internal structure of the branes where the 5D brane can be considered thin with respect to the 4D one. We consider the solutions corresponding to pure tension sources on the 4D brane, and study perturbations at first order around these background solutions. We adopt a 4D scalar-vector-tensor decomposition, and focus on the scalar sector of perturbations. We show that, in a suitable 4D limit, the trace part of the 4D metric perturbations obeys a decoupled equation which suggests that it is a ghost for background tensions smaller than a critical tension, while it is a healthy field otherwise. We give a geometrical interpretation of the existence of the critical tension and of the reason why the relevant field is a ghost or not depending on the background tension. We however find a value of the critical tension which is different from the one already found in the literature. Differently from the results in the literature, our analysis implies that, choosing the background tension suitably, we can construct ghost-free models for any value of the free parameters of the theory. We suggest that the difference lies in the procedure used to evaluate the pillbox integration across the codimension-2 brane. We confirm the validity of our analysis by performing numerically the integration in a particular case where the solution inside the thick cod-2 brane is known exactly. We stress that the singular structure of the perturbation fields in the nested branes set-ups is very subtle, and that great care has to be taken when deriving the codimension-2 junction conditions.
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