状态微分方程可积与不可积的FRW宇宙学模型
FRW cosmological models with integrable and nonintegrable differential equations of state
摘要：
现代宇宙学的基本模型在FRW时空中工作。因此，研究FRW宇宙学模型的物理和数学性质是非常重要的。在这项工作中，我们考虑FRW模型的状态微分方程。构造了几类新的可积和不可积FRW宇宙模型。值得注意的是，所有提出的可积和不可积FRW模型承认精确解。对于其中的一些，这样的精确解。还提出了一些人工二维FRW模型。最后，在附录中，我们推广了g-本质模型及其两个约化：k-本质和f-本质的结果。
英文摘要：
The basic models of modern cosmology work in FRW spacetime. Hence follows that it is important to study the physical and mathematical nature of FRW cosmological models. In this work, we consider FRW models with the differential equations of state. Some new classes integrable and nonintegrable FRW cosmological models were constructed. It is remarkable that all proposed integrable and nonintegrable FRW models admit exact solutions. For some of them, such exact solutions are presented. Some artificial two-dimensional FRW models were also proposed. Finally in Appendix, we extend the obtained results for g-essence models and for its two reductions: k-essence and f-essence.
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