铺砌空间与膨胀宇宙：连接量子力学与宇宙学
Tiling Spaces and the Expanding Universe: Bridging Quantum Mechanics and Cosmology
AI总结：
提出宇宙为高维晶格投影的生长准晶体模型，通过含时边界薛定谔方程推导类 Friedmann 方程，以准晶准粒子解释膨胀与暗物质，连接量子与宇宙学。
摘要：
我们提出一个启发式模型，将宇宙视为从高维晶格投影而来的生长准晶体。该准晶框架为宇宙膨胀提供了新视角，其内禀生长动力学自然地产生了观测到的大尺度宇宙膨胀。受此模型启发，我们探讨了具有含时边界的盒中粒子薛定谔方程，用以表示不断膨胀的底层空间。通过引入一个将微观量子现象与宏观宇宙学量相联系的约束，我们推导出一个类似于 Friedmann 方程的方程，为 Hubble tension 提供了潜在见解。我们的模型引入了 phonons 和 phasons——准晶结构固有的准粒子——它们在宇宙尺度动力学及宇宙膨胀中发挥关键作用。该框架表明，暴胀期的必要性可能被免除。此外，源自准晶结构的 phonons 可作为暗物质候选者，影响普通物质的动力学，同时在电磁相互作用中基本无法被探测。借鉴原子尺度上本质上为量子性的晶体物质，我们探讨了铺砌空间的概念如何在离散结构之上支撑连续对称性。这为理解宇宙膨胀及底层结构提供了新框架。因此，我们的方法表明，进一步发展可加深对宇宙膨胀与结构的理解，从而连接量子力学、凝聚态物理与宇宙学的概念。
英文摘要：
We propose a heuristic model of the universe as a growing quasicrystal projected from a higher-dimensional lattice. This quasicrystalline framework offers a novel perspective on cosmic expansion, where the intrinsic growth dynamics naturally give rise to the observed large-scale expansion of the universe. Motivated by this model, we explore the Schrödinger equation for a particle in a box with time-dependent boundaries, representing the expanding underlying space. By introducing a constraint that links microscale quantum phenomena with macroscale cosmological quantities, we derive an equation resembling the Friedmann equation, providing potential insights into the Hubble tension. Our model incorporates phonons and phasons-quasiparticles inherent in quasicrystalline structures-that play critical roles in cosmic-scale dynamics and the universe's expansion. This framework suggests that the necessity for an inflationary period may be obviated. Furthermore, phonons arising from the quasicrystalline structure may serve as dark matter candidates, influencing the dynamics of ordinary matter while remaining largely undetectable through electromagnetic interactions. Drawing parallels with crystalline matter at atomic scales, which is fundamentally quantum in nature, we explore how the notion of tiling space can support continuous symmetry atop a discrete structure. This provides a novel framework for understanding the universe's expansion and underlying structure. Consequently, our approach suggests that further development could enhance our understanding of cosmic expansion and the universe's structure, bridging concepts from quantum mechanics, condensed matter physics, and cosmology.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
