Cosmological models can be studied effectively using dynamical systems techniques. Starting from Brown’s formulation of the variational principle for relativistic fluids, we introduce new types of couplings involving a perfect fluid, a scalar field, and boundary terms. We describe three different coupling models, one of which turns out to be particularly relevant for cosmology. Its behaviour is similar to that of models in which dark matter decays into dark energy. In particular, for a constant coupling, the model mimics well-known dynamical dark energy models while the non-constant couplings offer a rich dynamical structure, unseen before. We are able to achieve this richness whilst working in a two-dimensional phase space. This is a significant advantage which allows us to provide a clear physical interpretation of the key features and draw analogies with previously studied models.

使用动力系统技术可以有效地研究宇宙学模型。从布朗对相对论流体变分原理的阐述开始，我们引入了涉及完美流体、标量场和边界项的新型耦合。我们描述了三种不同的耦合模型，其中一种与宇宙学特别相关。其行为类似于暗物质衰变成暗能量的模型。特别是，对于恒定耦合，该模型模仿了众所周知的动态暗能量模型，而非恒定耦合则提供了以前从未见过的丰富的动态结构。我们能够在二维相空间中工作时实现这种丰富性。这是一个显着的优势，它使我们能够对关键特征提供清晰的物理解释，并与之前研究的模型进行类比。