标题： 洛伦兹量子宇宙学和超普朗克物理中不存在平滑时空 显示英文标题

标题： No Smooth Spacetime in Lorentzian Quantum Cosmology and Trans-Planckian Physics

摘要： 在极小超空间量子宇宙学中，无边界和隧穿提案的洛伦兹路径积分公式最近已被分析。 但已经指出，在均匀且各向同性背景周围的线性化扰动波函数呈反高斯形式，因此它们的相关函数是发散的。 在本文中，我们重新审视这一问题，并通过基于超越普朗克物理的色散关系修改来考虑洛伦兹量子宇宙学中的扰动问题。 我们以两种修改后的色散关系为例，即包含更高动量项的广义Corley-Jacobson色散关系和具有超越普朗克模式截断的Unruu色散关系。 我们表明，通过在短距离处修改色散关系的超越普朗克物理难以克服洛伦兹量子宇宙学中扰动的反高斯问题。 显示英文摘要

摘要： In minisuperspace quantum cosmology, the Lorentzian path integral formulations of the no-boundary and tunneling proposals have recently been analyzed. But it has been pointed out that the wave function of linearized perturbations around a homogeneous and isotropic background is of an inverse Gaussian form and thus that their correlation functions are divergent. In this paper, we revisit this issue and consider the problem of perturbations in Lorentzian quantum cosmology by modifying the dispersion relation based on trans-Planckian physics. We consider two modified dispersion relations, the generalized Corley-Jacobson dispersion relation with higher momentum terms and the Unruh dispersion relation with a trans-Planckian mode cut-off, as examples. We show that the inverse Gaussian problem of perturbations in Lorentzian quantum cosmology is hard to overcome with the trans-Planckian physics modifying the dispersion relation at short distances.