标题： 一般暗能量理论的非线性重构 显示英文标题

标题： Nonlinear reconstruction of general dark energy theories

摘要： 暗能量（DE）理论的多样性和数量使得逐一进行详细分析不切实际，这促使人们提出“参数化”理论的方法，以缩小理论空间的规模。 解决这一问题的主要方法是暗能量的有效场论（EFTofDE），它可以使用少量可观察的时间依赖函数来描述一般的霍恩德斯基类型理论。 然而，EFTofDE主要适用于线性扰动，而对于需要筛选机制的理论来说，将其扩展为完全非线性的描述具有挑战性。 在本文中，我们提出了一种通用方法，从背景膨胀历史和某些线性扰动量中重建非线性DE拉格朗日量，该方法建立在EFTofDE框架之上。 通过数值例子，我们证明了该方法适用于广泛的单标量场暗能量和修改引力理论，包括量子能、标量-张量理论、$k$-essence以及具有平移对称性的广义三次伽利略理论。 对于这些理论中的每一种，我们讨论了该方法的有效性以及影响其结果的因素。 虽然该方法涉及求解微分方程，但我们发现初始条件对于量子能、标量-张量理论和$k$-essence并不重要，而对于具有平移对称性的三次伽利略理论，通用跟踪解可以帮助将微分方程转化为代数方程。 这提供了一个有用的框架，将背景和线性扰动水平的宇宙学观测与暗能量的底层非线性动力学联系起来，并将使宇宙学模拟能够系统且更详细地分析和检验DE理论。 显示英文摘要

摘要： The large variety and number of dark energy (DE) theories make it impractical to perform detailed analyses on a case-by-case basis, which has motivated proposals to ``parameterize" theories to reduce the size of theory space. The leading approach to do this is the effective field theory of dark energy (EFTofDE), which can describe general Horndeski-type theories with a small number of observationally accessible time-dependent functions. However, the EFTofDE primarily works for linear perturbations, and extending it to obtain a fully non-linear description of DE theories, which is critical for theories with screening mechanisms, is challenging. In this paper, we present a general method for reconstructing the non-linear DE Lagrangian from the background expansion history and certain linear-perturbation quantities, building upon the EFTofDE framework. Using numerical examples, we demonstrate that this method is applicable to a wide range of single-scalar-field dark energy and modified gravity theories, including quintessence, scalar-tensor theory, $k$-essence, and generalized cubic Galileon with shift symmetry. For each of these theories, we discuss the validity of the method and factors affecting its results. While this method involves solving differential equations, we find that the initial conditions are not important for quintessence, scalar-tensor theory and $k$-essence, while for shift-symmetric cubic Galileon, the generic tracker solution can help transform differential equations into algebraic equations. This offers a useful framework to connect cosmological observations at the background and linear-perturbation levels to the underlying non-linear dynamics of dark energy, and will enable cosmological simulations to analyze and examine DE theories systematically and in much greater detail.