A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious challenges of modern cosmology and of particle physics have motivated the exploration of further generalised theories of spacetime. Even though Einstein's interpretation of gravity in terms of the curvature of spacetime is commonly adopted, the assignment of geometrical concepts to gravity is ambiguous because General Relativity allows three entirely different, but equivalent approaches of which Einstein's interpretation is only one. From a field-theoretical perspective, however, the construction of a consistent theory for a Lorentz-invariant massless spin-2 particle uniquely leads to General Relativity. Keeping Lorentz invariance then implies that any modification of General Relativity will inevitably introduce additional propagating degrees of freedom into the gravity sector. Adopting this perspective, we will review the recent progress in constructing consistent field theories of gravity based on additional scalar, vector and tensor fields. Within this conceptual framework, we will discuss theories with Galileons, with Lagrange densities as constructed by Horndeski and beyond, extended to DHOST interactions, or containing generalized Proca fields and extensions thereof, or several Proca fields, as well as bigravity theories and scalar-vector-tensor theories. We will review the motivation of their inception, different formulations, and essential results obtained within these classes of theories together with their empirical viability.

中文翻译：

---

广义相对论及其宇宙学含义的系统化方法

一个世纪前，爱因斯坦提出了他优雅而精致的广义相对论理论，迄今为止，该理论经受住了大量的实证检验，并取得了显着的成功。尽管爱因斯坦的理论取得了胜利，但现代宇宙学和粒子物理学的顽强挑战激发了对时空的进一步广义理论的探索。尽管爱因斯坦根据时空曲率对引力的解释被普遍采用，但将几何概念分配给引力是模棱两可的，因为广义相对论允许三种完全不同但等效的方法，而爱因斯坦的解释只是其中一种。然而，从场论的角度来看，洛伦兹不变的无质量自旋 2 粒子的一致性理论的构建独特地导致了广义相对论。保持洛伦兹不变性意味着广义相对论的任何修改都将不可避免地将额外的传播自由度引入重力扇区。采用这种观点，我们将回顾最近在基于附加标量、矢量和张量场构建一致的引力场理论方面取得的进展。在这个概念框架内，我们将讨论伽利略理论，包括由 Horndeski 及其他人构建的拉格朗日密度，扩展到 DHOST 相互作用，或包含广义 Proca 域及其扩展，或几个 Proca 域，以及大引力理论和标量向量-张量理论。我们将回顾他们成立的动机，