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arXiv 0909.1079hep-thastro-ph.COgr-qc
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高阶膜引力模型

Higher-order brane gravity models

Mariusz P. Dabrowski, Adam Balcerzak

摘要:

我们讨论一个非常一般的引力理论,其中拉格朗日是一个任意函数的曲率不变量,在膜上。一般来说,结条件的公式化(除了欧拉特征,如高斯-邦纳项)导致δ函数的幂,需要正则化。我们建议避免这样一个问题的方法是,强制度规及其一阶导数在膜上是正则的,二阶导数有一个扭结,度规的三阶导数有一个阶跃函数不连续性,并且不迟于度规的四阶导数给场方程的δ函数贡献。另外,我们通过引入额外的标量场和张量场:标量子和张量子,讨论了四阶引力到二阶引力的约化。为了获得交界条件,我们采用两种方法:应用高斯-Codazzi形式主义和应用广义Gibbons-Hawking边界项,附加到适当的行动。在最一般的情况下,我们推导出结的条件,而不假设连续的标量和张量的膜上。导出的结条件可以用于研究高阶膜引力模型的宇宙学意义。

英文摘要:

We discuss a very general theory of gravity, of which Lagrangian is an arbitrary function of the curvature invariants, on the brane. In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the powers of the delta function and requires regularization. We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to the field equations. Alternatively, we discuss the reduction of the fourth-order gravity to the second order theory by introducing extra scalar and tensor fields: the scalaron and the tensoron. In order to obtain junction conditions we apply two methods: the application of the Gauss-Codazzi formalism and the application of the generalized Gibbons-Hawking boundary terms which are appended to the appropriate actions. In the most general case we derive junction conditions without assuming the continuity of the scalaron and the tensoron on the brane. The derived junction conditions can serve studying the cosmological implications of the higher-order brane gravity models.

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