The generalised Proca (GP) theory is a modified gravity model in which the acceleration of the cosmic expansion rate can be explained by self interactions of a cosmological vector field. In this paper we study a particular sub-class of the GP theory, with up to cubic order Lagrangian, known as the cubic vector Galileon (cvG) model. This model is similar to the cubic scalar Galileon (csG) in many aspects, including a fifth force and the Vainshtein screening mechanism, but with the additional flexibility that the strength of the fifth force depends on an extra parameter — interpolating between zero and the full strength of the csG model — while the background expansion history is independent of this parameter. It offers an interesting alternative to ΛCDM in explaining the cosmic acceleration, as well as a solution to the tension between early- and late-time measurements of the Hubble constant H ₀. To identify the best ways to test this model, in this paper we conduct a comprehensive study of the phenomenology of this model in the nonlinear regime of large-scale structure formation, using a suite of N-body simulations run with the modified gravity code ECOSMOG. By inspecting thirteen statistics of the dark matter field, dark matter haloes and weak lensing maps, we find that the fifth force in this model can have particularly significant effects on the large-scale velocity field and lensing potential at late times, which suggest that redshift-space distortions and weak lensing can place strong constraints on it.

广义普罗卡 (GP) 理论是一种修正的引力模型，其中宇宙膨胀率的加速可以通过宇宙矢量场的自相互作用来解释。在本文中，我们研究了 GP 理论的一个特定子类，具有高达三次阶的拉格朗日，称为三次向量伽利略 (cvG) 模型。该模型在许多方面类似于三次标量伽利略 (csG)，包括第五力和 Vainshtein 筛选机制，但具有额外的灵活性，即第五力的强度取决于一个额外的参数 - 在零和全csG 模型的强度——而背景扩展历史与此参数无关。它提供了一个有趣的替代 ΛCDM 来解释宇宙加速的方法，H ₀。为了确定测试该模型的最佳方法，在本文中，我们使用一组 N 体模拟，使用修改后的重力代码 ECOSMOG . 通过检查暗物质场、暗物质晕和弱透镜图的 13 个统计数据，我们发现该模型中的第五力可以对后期的大尺度速度场和透镜势产生特别显着的影响，这表明红移- 空间扭曲和弱透镜会对它施加强烈的限制。