We leverage powerful mathematical tools stemming from optimal transport theory and transform them into an efficient algorithm to reconstruct the fluctuations of the primordial density field, built on solving the Monge-Amp\`ere-Kantorovich equation. Our algorithm computes the optimal transport between an initial uniform continuous density field, partitioned into Laguerre cells, and a final input set of discrete point masses, linking the early to the late Universe. While existing early universe reconstruction algorithms based on fully discrete combinatorial methods are limited to a few hundred thousand points, our algorithm scales up well beyond this limit, since it takes the form of a well-posed smooth convex optimization problem, solved using a Newton method. We run our algorithm on cosmological $N$-body simulations, from the AbacusCosmos suite, and reconstruct the initial positions of $\mathcal{O}(10^7)$ particles within a few hours with an off-the-shelf personal computer. We show that our method allows a unique, fast and precise recovery of subtle features of the initial power spectrum, such as the baryonic acoustic oscillations.

翻译：我们利用来自最佳运输理论的强大数学工具,将其转化为高效的算法,以重建原始密度域的波动,该算法建立在解决蒙古-安普-埃雷-坎托罗维奇方程式的基础上。我们的算法计算了最初统一连续密度场之间的最佳迁移,将其分割成拉古雷电池,以及一组离散点质量的最后输入,将早期与后宇宙连接起来。虽然基于完全离散的组合式方法的现有早期宇宙重建算法限于几百万个点,但我们的算法规模远远超过了这一限度,因为其形式是用牛顿法解决的精巧的平滑 convex优化问题。我们从AbacusCosmospace套件中运行了我们关于宇宙学 $N$-体模拟的算法,并用离散的个人计算机在几个小时内重建$\mathcal{O}(10 ⁇ 7)$的初始位置。我们的方法可以使初始能量频谱的精细特征(例如巴调的声波层)得到独特、快速和精确的恢复。