一类$f(R)$模型的物理非生存性及其常曲率解
Physical non-viability of a wide class of $f(R)$ models and their constant-curvature solutions
摘要：
常曲率解是引力物理学的核心，史瓦西和（反）-德西特是两个最典型的例子。虽然这种解在广义相对论中非常有名，但爱因斯坦范式之外的引力理论却并非如此。在这篇文章中，我们提供了一个系统的概述$f(R)$模型允许常数曲率的解决方案，以及常数曲率的解决方案本身。我们的结论是，这些$f(R)$模型的绝大多数遭受，一般来说，从几个缺点，使其可行性非常有限，当不排除物理证据。这些缺陷包括不稳定性（包括以前无法预见的强耦合问题）和限制模型预测能力的问题。此外，我们还将表明，大多数$f(R)$排他的常曲率解也表现出各种非物理性质。
英文摘要：
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.
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