We consider a cosmological scenario endowed with an interaction between the universe’s dark components – dark matter and dark energy. Specifically, we assume the dark matter component to be a pressure-less fluid, while the dark energy component is a quintessence scalar field with Lagrangian function modified by the quadratic Generalized Uncertainty Principle. The latter modification introduces new higher-order terms of fourth-derivative due to quantum corrections in the scalar field’s equation of motion. Then, we investigate asymptotic dynamics and general behaviour of solutions of the field equations for some interacting models of special interests in the literature. At the background level, the present interacting model exhibits the matter-dominated and de Sitter solutions which are absent in the corresponding quintessence model. Furthermore, to boost the background analysis, we study cosmological linear perturbations in the Newtonian gauge where we show how perturbations are modified by quantum corrected terms from the quadratic Generalized Uncertainty Principle. Depending on the coupling parameters, scalar perturbations show a wide range of behavior.

我们考虑一个宇宙场景，它赋予了宇宙暗成分——暗物质和暗能量之间的相互作用。具体来说，我们假设暗物质成分是一种无压力的流体，而暗能量成分是具有经二次广义不确定性原理修正的拉格朗日函数的典型标量场。由于标量场运动方程中的量子校正，后一种修改引入了四阶导数的新高阶项。然后，我们研究了文献中一些特别感兴趣的相互作用模型的场方程解的渐近动力学和一般行为。在背景层面，本交互模型展示了相应的精华模型中不存在的物质主导解和德西特解。此外，为了加强背景分析，我们研究了牛顿规范中的宇宙学线性扰动，在那里我们展示了如何通过二次广义不确定性原理中的量子校正项修改扰动。根据耦合参数，标量扰动表现出广泛的行为。