Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension (SME) has been widely used as a phenomenological framework in investigations of spacetime symmetry breaking. Until recently, it was thought that the SME was suitable only for theories with spontaneous spacetime symmetry breaking due to consistency conditions stemming from the Bianchi identities. However, it has recently been shown that, particularly with matter couplings included, the consistency conditions can also be satisfied in theories with explicit breaking. An overview of how this is achieved is presented, and two examples are examined. The first is massive gravity, which includes a nondynamical background tensor. The second is a model based on a low-energy limit of Hořava gravity, where spacetime has a physically preferred foliation. In both cases, bounds on matter–gravity interactions that explicitly break diffeomorphisms are obtained using the SME.

中文翻译：

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引力与显式同构分解

十多年来，人们一直使用修改后的引力理论来明确打破微分不变性，以探索与量子引力，暗能量和暗物质有关的未解决问题。同时，标准模型扩展（SME）已被广泛用作时空对称性破坏研究的现象学框架。直到最近，人们仍认为SME仅适用于由于Bianchi身份产生的一致性条件而导致自发的时空对称性破裂的理论。但是，最近显示出，特别是在包括物质耦合的情况下，在理论上也可以通过显式破坏来满足一致性条件。概述了如何实现此目标，并研究了两个示例。首先是巨大的引力，其中包括非动态背景张量。第二种是基于Hořava重力的低能量极限的模型，其中时空在物理上是首选的叶状结构。在这两种情况下，都可以使用SME来确定物质-重力相互作用的界限，从而明确地打破了微分同构。