Brane gravity, higher derivative terms, and nonlocality
Brane gravity, higher derivative terms, and nonlocality
复制标题
膜引力、高阶导数项和非定域性
DOI：
10.1103/physrevd.65.084036
复制
发表时间：
2001
影响因子：
5
通讯作者：
S. Mukohyama
中科院分区：
文献类型：
--
作者：
S. Mukohyama
在薄膜世界的场景中，在两个薄膜之间有一个整体标量场，众所周知，四维爱因斯坦引力在两个薄膜中的任何一个上以低能量恢复。通过使用规范不变的引力和标量微扰形式，我们将薄膜世界中的弱引力理论推广到更高的能量，或更短的距离。我们认为，如果膜间距离(弧度)是稳定的，背景体标量场在膜附近发生变化，并且膜附近的背景体几何形状是翘曲的，则任一膜上的弱重力与4维高导数重力是不可区分的。这一论点适用于到标架的一般保角变换，在该标架中，膜上的物质最小限度地耦合到度规。特别地，确定了四维有效作用中的牛顿常数和曲率平方项系数，直到增加一个Gauss-Bonnet拓扑项的模糊性。换句话说，我们提供了所谓的$R^2$模型的膜世界实现，而不使用量子理论。我们讨论了除了薄膜上的引力子外，还出现了自旋2和自旋0的复合场，并指出自旋0场可能起到有效膨胀粒子的作用来驱动薄膜世界的膨胀。最后，我们猜想高阶导数项序列是一个无穷级数，从而表明在膜世界场景中的非局部性。
In brane world scenarios with a bulk scalar field between two branes it is known that 4-dimensional Einstein gravity is restored at low energies on either brane. By using a gauge-invariant gravitational and scalar perturbation formalism we extend the theory of weak gravity in the brane world scenarios to higher energies, or shorter distances. We argue that weak gravity on either brane is indistinguishable from 4-dimensional higher derivative gravity, provided that the inter-brane distance (radion) is stabilized, that the background bulk scalar field is changing near the branes and that the background bulk geometry near the branes is warped. This argument holds for a general conformal transformation to a frame in which matter on the branes is minimally coupled to the metric. In particular, Newton's constant and the coefficients of curvature-squared terms in the 4-dimensional effective action are determined up to an ambiguity of adding a Gauss-Bonnet topological term. In other words, we provide the brane-world realization of the so called $R^2$-model without utilizing a quantum theory. We discuss the appearance of composite spin-2 and spin-0 fields in addition to the graviton on the brane and point out a possibility that the spin-0 field may play the role of an effective inflaton to drive brane-world inflation. Finally, we conjecture that the sequence of higher derivative terms is an infinite series and, thus, indicates non-locality in the brane world scenarios.