This review is a pedagogical introduction to models of gravity and how they are constrained through cosmological observations. We focus on the Horndeski scalar-tensor theory and on the quantities that can be measured with a minimum of assumptions. Alternatives or extensions of general relativity have been proposed ever since its early years. Because of the Lovelock theorem, modifying gravity in four dimensions typically means adding new degrees of freedom. The simplest way is to include a scalar field coupled to the curvature tensor terms. The most general way of doing so without incurring in the Ostrogradski instability is the Horndeski Lagrangian and its extensions. Testing gravity means therefore, in its simplest term, testing the Horndeski Lagrangian. Since local gravity experiments can always be evaded by assuming some screening mechanism or that baryons are decoupled, or even that the effects of modified gravity are visible only at early times, we need to test gravity with cosmological observations in the late universe (large-scale structure) and in the early universe (cosmic microwave background). In this work, we review the basic tools to test gravity at cosmological scales, focusing on model-independent measurements.

中文翻译：

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在宇宙尺度上测量重力

这篇评论是对引力模型的教育学介绍，以及如何通过宇宙学观测来限制引力模型。我们专注于Horndeski标量-张量理论和最少假设即可测​​量的数量。自从相对论以来，就已经提出了相对论的替代或扩展。由于洛夫洛克定理，在四个维度上修改引力通常意味着增加新的自由度。最简单的方法是包括一个与曲率张量项耦合的标量场。不会导致Ostrogradski不稳定的最通用方法是Horndeski Lagrangian及其扩展名。因此，测试重力意味着用最简单的术语测试Horndeski Lagrangian。由于总是可以通过假设某种筛选机制来逃避局部引力实验，或者可以忽略重子，或者甚至只有在较早的时候才能看到重心的影响，因此我们需要在宇宙后期通过宇宙学观测来测试引力（大规模结构）和早期宇宙（宇宙微波背景）。在这项工作中，我们回顾了在宇宙学尺度上测试重力的基本工具，重点是与模型无关的测量。