We derive a theory-independent version of the momentum constraint equation for use in cosmology, as a part of the parameterised post-Newtonian cosmology framework. Our equations are constructed by adapting the corresponding quantities from formalisms constructed for testing and constraining gravity in isolated astrophysical systems, thereby extending the domain of applicability of these approaches up to cosmological scales. Our parameterised equations include both scalar and divergenceless-vector gravitational potentials, and can be applied to both conservative and non-conservative theories of gravity. They can also be used to describe the gravitational fields of both non-linear structures and super-horizon perturbations. We apply the parameterised equations we propose to quintessence models of dark energy, as well as scalar-tensor and vector-tensor theories of gravity. We find them to work well in each case. Our equations are highly compact, and are intended to be useful for constraining gravity in a theory-independent fashion in cosmology.

中文翻译：

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参数化后牛顿宇宙学中的动量约束方程

作为参数化后牛顿宇宙学框架的一部分，我们推导出了一个用于宇宙学的动量约束方程的独立于理论的版本。我们的方程式是通过调整为在孤立的天体物理系统中测试和约束引力而构建的形式主义的相应数量来构建的，从而将这些方法的适用范围扩展到宇宙尺度。我们的参数化方程包括标量和无散矢量引力势，可以应用于保守和非保守引力理论。它们还可以用来描述非线性结构和超视距扰动的引力场。我们将我们提出的参数化方程应用于暗能量的精粹模型，以及引力的标量张量和矢量张量理论。我们发现它们在每种情况下都能很好地工作。我们的方程非常紧凑，旨在以独立于理论的方式在宇宙学中用于约束引力。