极限曲率拟引力是有效的聚合物量子引力吗？
Is limiting curvature mimetic gravity an effective polymer quantum gravity?
摘要：
最近提出的一个版本的拟引力通过依赖于标量场的达朗伯的特定势，将极限曲率纳入了广义相对论。在均匀和各向同性的情况下，一旦极限曲率被确定为普朗克尺度的倍数，所得到的理论就与有效圈量子宇宙学（LQC）的最简单化身一致。在本文中，我们回答的问题，这样的关系是否可以举行的情况下，比安基我模型。结果是否定的：由于在LQC下的聚合物希尔伯特空间中出现了不能支持的项，因此不可能将极限曲率拟引力的哈密顿量视为有效的LQC哈密顿量。本分析补充了球对称背景下的相关结果。
英文摘要：
A recently proposed version of mimetic gravity incorporates a limiting curvature into general relativity by means of a specific potential depending on the d'Alembertian of the scalar field. In the homogeneous and isotropic setting, the resulting theory agrees with the simplest incarnation of effective loop quantum cosmology (LQC) once the limiting curvature is identified with a multiple of the Planck scale. In this paper, we answer the question of whether such a relation can hold in the context of Bianchi I models. Our result is negative: it turns out to be impossible to view the Hamiltonian of limiting curvature mimetic gravity as an effective LQC Hamiltonian due to the appearance of terms that cannot be supported on the polymer Hilbert space underlying LQC. The present analysis complements a related result in the context of spherical symmetry.
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