标题： 一类$f(R)$模型及其常曲率解的物理不可行性 显示英文标题

标题： Physical non-viability of a wide class of $f(R)$ models and their constant-curvature solutions

摘要： 常曲率解位于引力物理学的核心，史瓦西解和（反）德西特解是其中两个最典型的例子。 尽管这类解在广义相对论中非常为人所知，但对于超出爱因斯坦框架的引力理论来说并非如此。 本文系统地综述了允许常曲率解的$f(R)$模型以及这些常曲率解本身。 我们得出结论，大多数这些$f(R)$模型通常存在一些缺陷，使得它们的可行性极为有限，甚至可能被物理证据排除。 这些缺陷包括不稳定性（包括之前未预见的强耦合问题）和限制模型预测能力的问题。 此外，我们还将展示大多数$f(R)$-专属的常曲率解也表现出各种非物理性质。 显示英文摘要

摘要： Constant-curvature solutions lie at the very core of gravitational physics, with Schwarzschild and (Anti)-de Sitter being two of the most paradigmatic examples. Although such kind of solutions are very well-known in General Relativity, that is not the case for theories of gravity beyond the Einsteinian paradigm. In this article, we provide a systematic overview on $f(R)$ models allowing for constant-curvature solutions, as well as of the constant-curvature solutions themselves. We conclude that the vast majority of these $f(R)$ models suffer, in general, from several shortcomings rendering their viability extremely limited, when not ruled out by physical evidence. Among these deficiencies are instabilities (including previously unforeseen strong-coupling problems) and issues limiting the predictive power of the models. Furthermore, we will also show that most $f(R)$-exclusive constant-curvature solutions also exhibit a variety of unphysical properties.