The little rip is a cosmological abrupt event predicted by some phantom dark energy models that could describe the future evolution of our Universe. This event can be interpreted as a big rip singularity delayed indefinitely, although in those models bounded structures will be destroyed in a finite cosmic time in the future. In this work, we analyze the little rip cosmology from a classical and quantum point of view within the scheme of alternative metric $f(R)$ theories of gravity. The quantum analysis is performed in the framework of $f(R)$ quantum geometrodynamics by means of the modified Wheeler-DeWitt equation. In this context, we show that the DeWitt criterion can be satisfied. Similar to what happens in general relativity, this result points toward the avoidance of the little rip in $f(R)$ quantum cosmology.

中文翻译：

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经典和量子f(R)宇宙学的小裂痕

小裂口是由一些幻影暗能量模型预测的宇宙学突然事件，可以描述我们宇宙的未来演化。这一事件可以被解释为一个无限期延迟的大撕裂奇点，尽管在这些模型中，有界结构将在未来有限的宇宙时间内被摧毁。在这项工作中，我们在替代度量方案中从经典和量子的角度分析了小裂隙宇宙学$F(\mathrm{电阻})$重力理论。量子分析是在以下框架中进行的$F(\mathrm{电阻})$量子几何动力学通过修正的惠勒-德威特方程。在这种情况下，我们表明可以满足 DeWitt 准则。与广义相对论中发生的情况类似，该结果表明避免了$F(\mathrm{电阻})$ 量子宇宙学。