Hořava gravity breaks Lorentz symmetry by introducing a dynamical timelike scalar field (the khronon), which can be used as a preferred time coordinate (thus selecting a preferred space–time foliation). Adopting the khronon as the time coordinate, the theory is invariant only under time reparametrizations and spatial diffeomorphisms. In the infrared limit, this theory is sometimes referred to as khronometric theory. Here, we explicitly construct a generalization of khronometric theory, which avoids the propagation of Ostrogradski modes as a result of a suitable degeneracy condition (although stability of the latter under radiative corrections remains an open question). While this new theory does not have a general-relativistic limit and does not yield a Friedmann–Robertson–Walker-like cosmology on large scales, it still passes, for suitable choices of its coupling constants, local tests on Earth and in the Solar System, as well as gravitational-wave tests. We also comment on the possible usefulness of this theory as a toy model of quantum gravity, as it could be completed in the ultraviolet into a ‘degenerate Hořava gravity’ theory that could be perturbatively renormalizable without imposing any projectability condition.

Hořava 引力通过引入动态类时标量场（khronon）打破了洛伦兹对称性，该标量场可用作首选时间坐标（从而选择首选时空叶理）。采用khronon作为时间坐标，该理论只有在时间重参数化和空间微分同胚下才具有不变性。在红外极限中，这个理论有时被称为测时理论。在这里，我们明确地构建了测时理论的概括，它避免了由于合适的简并条件而导致的 Ostrogradski 模式的传播（尽管后者在辐射校正下的稳定性仍然是一个悬而未决的问题）。虽然这个新理论没有广义相对论的限制，也没有在大尺度上产生类似弗里德曼-罗伯逊-沃克的宇宙学，但它仍然通过，其耦合常数的合适选择，地球和太阳系的局部测试，以及引力波测试。我们还评论了该理论作为量子引力的玩具模型的可能用途，因为它可以在紫外线中完成为“退化的 Hořava 引力”理论，该理论可以在不施加任何可投影性条件的情况下进行微扰重整化。