In this paper, we discuss singularity theorems in quantum gravity using effective field theory methods. To second order in curvature, the effective field theory contains two new degrees of freedom which have important implications for the derivation of these theorems: a massive spin-2 field and a massive spin-0 field. Using an explicit mapping of this theory from the Jordan frame to the Einstein frame, we show that the massive spin-2 field violates the null energy condition, while the massive spin-0 field satisfies the null energy condition, but may violate the strong energy condition. Due to this violation, classical singularity theorems are no longer applicable, indicating that singularities can be avoided, if the leading quantum corrections are taken into account.

中文翻译：

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有效场论中曲率二阶量子引力的奇异性定理

在本文中，我们使用有效的场论方法讨论了量子引力中的奇异性定理。对于曲率的二阶，有效场论包含两个新的自由度，它们对这些定理的推导具有重要意义：一个大的自旋2场和一个大的自旋0场。使用从Jordan框架到Einstein框架的该理论的显式映射，我们表明，自旋2场违反了零能条件，而自旋0场满足了零能条件，但可能违反了强能。健康）状况。由于这种违反，经典奇异性定理不再适用，表明如果考虑领先的量子校正，就可以避免奇异性。