Monge Ampère引力：从大偏差原理到基于最优输运的宇宙学模拟
Monge Ampère gravity: from the large deviation principle to cosmological simulations through optimal transport
AI总结：
本研究基于最优输运理论探究Monge-Ampère引力的宇宙结构形成效应，推导其从布朗粒子系统大偏差原理的涌现过程，开发半离散最优输运N体模拟方法，验证其大、小尺度的结构形成特性，算法可推广至同类修正引力模拟。
摘要：
我们将Monge-Ampère引力（MAG）作为一种宇宙结构形成的有效理论，通过最优输运理论开展研究。MAG基于Monge-Ampère方程——泊松方程的一种非线性形式，该方程将势的海森行列式与密度场关联起来。我们阐释了在连续极限下，MAG如何通过大偏差原理，从由独立且全同的布朗粒子构成的受约束系统中涌现。为对这一高度非线性理论进行数值探究，我们开发了一种基于半离散最优输运的新型N体模拟方法。我们从首次开展的、包含超1亿个粒子的Monge-Ampère引力N体模拟中得到的结果显示：在大尺度上，Monge-Ampère引力与牛顿引力相似，但更倾向于形成纤维状等各向异性结构；在小尺度上，MAG的成团性更弱，且在高密度区域会被屏蔽。尽管我们在此将Monge-Ampère引力作为有效理论而非基础理论进行研究，但我们提出的新型高性能最优输运算法可用于运行一大类修正引力理论的高分辨率模拟，例如Galileons理论，这类理论的运动方程为二阶且属于Monge-Ampère型。
英文摘要：
We study Monge-Ampère gravity (MAG) as an effective theory of cosmological structure formation through optimal transport theory. MAG is based on the Monge-Ampère equation, a nonlinear version of the Poisson equation, that relates the Hessian determinant of the potential to the density field. We explain how MAG emerges from a conditioned system of independent and indistinguishable Brownian particles, through the large deviation principle, in the continuum limit. To numerically explore this highly non-linear theory, we develop a novel N-body simulation method based on semi-discrete optimal transport. Our results obtained from the very first N-body simulation of Monge-Ampère gravity with over 100 millions particles show that on large scales, Monge-Ampère gravity is similar to the Newtonian gravity but favours the formation of anisotropic structures such as filaments. At small scales, MAG has a weaker clustering and is screened in high-density regions. Although here we study the Monge-Ampère gravity as an effective rather than a fundamental theory, our novel highly-performant optimal transport algorithm can be used to run high-resolution simulations of a large class of modified theories of gravity, such as Galileons, in which the equations of motion are second-order and of Monge-Ampère type.
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