更高的曲率修正能解决f（R）引力的奇异性问题吗？
Can higher curvature corrections cure the singularity problem in f(R) gravity?
摘要：
虽然$f(R)$修正的引力模型可以满足太阳系和宇宙学的约束，但它们的严重缺陷是不存在强引力场的恒星。本文讨论了高曲率修正是否能一致地纠正这种不存在性。下面的问题被证明是出现的成本必须支付的$f(R)$模型，允许中子星：（一）领先的校正必须微调有典型的能量标度$μ\lesssim 10^{-19}$ GeV，这基本上来自于相对论性恒星的自由降落时间;（二）领先的校正必须进一步微调，使其不是由二次曲率项。第二个问题是由于出现了一个中间曲率尺度，实验室重力实验将受到更高曲率改正的影响。因此，我们的分析意味着，这是一个挑战，构建可行的$f(R)$模型没有非常仔细和不自然的微调。
英文摘要：
Although $f(R)$ modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the $f(R)$ models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale $μ\lesssim 10^{-19}$ GeV, which essentially comes from the free fall time of a relativistic star; (ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable $f(R)$ models without very careful and unnatural fine-tuning.
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