印度金奈数学研究所Yadav, Gopal团队研究了慢滚膨胀和其他宇宙学中的无边界极值曲面。这一研究成果于2025年3月26日发表在《高能物理杂志》上。

在先前关于锚定在未来边界的德西特极值曲面的工作的基础上，课题组研究了慢滚膨胀模型中的无边界极值曲面，其中无边界全局dS的扰动保持了空间等距性。虽然在纯德西特空间中，欧几里德半球给出了一个等于德西特熵一半的实面积，但这里的无边界极值表面积总体上有非平凡的实部和虚部。

研究组评估了定义适当轮廓的复时间平面中的面积积分。对于4毫米的情况，慢滚参数中前导阶的实和虚有限修正与波函数（或作用）的半经典展开中的修正相匹配，并证实了之前讨论的宇宙膜解释。他们还研究了其他宇宙学中的无边界极值曲面，包括三维膨胀和小质量的史瓦西-德西特空间。

附：英文原文

Title: No-boundary extremal surfaces in slow-roll inflation and other cosmologies

Author: Goswami, Kaberi, Narayan, K., Yadav, Gopal

Issue&Volume: 2025-03-26

Abstract: Building on previous work on de Sitter extremal surfaces anchored at the future boundary, we study no-boundary extremal surfaces in slow-roll inflation models, with perturbations to no-boundary global dS preserving the spatial isometry. While in pure de Sitter space the Euclidean hemisphere gives a real area equalling half de Sitter entropy, the no-boundary extremal surface areas here have nontrivial real and imaginary pieces overall. We evaluate the area integrals in the complex time-plane defining appropriate contours. For the 4-dim case, the real and imaginary finite corrections at leading order in the slow-roll parameter match those in the semiclassical expansion of the Wavefunction (or action), and corroborate the cosmic brane interpretation discussed previously. We also study no-boundary extremal surfaces in other cosmologies including 3-dimensional inflation and Schwarzschild de Sitter spaces with small mass.

DOI: 10.1007/JHEP03(2025)193

Source: https://link.springer.com/article/10.1007/JHEP03(2025)193