某些可积和不可积FRW宇宙学模型中的暗能量
Dark energy in some integrable and nonintegrable FRW cosmological models
摘要：
当今宇宙学最大的挑战之一是确定暗能量的性质，暗能量是目前观测到的宇宙加速的来源。除了真空能之外，各种各样的暗能量模型也被提出。Friedmann-Robertson- Walker（FRW）时空在现代宇宙学中起着重要的作用.特别是，最流行的暗能量模型在FRW时空中工作。本文提出了一类新的可积FRW宇宙模型。这些模型由著名的Painlev $\acute{e}$方程导出。一些不可积的FRW模型也被考虑。这些最后的模型构造的帮助下Pinney，Schr $\ddot{o}$ dinger和超几何方程。本文给出了一些宇宙学模型的标量场描述和二维推广。最后构造了可积和不可积的$F(R)$和$F(G)$引力模型。
英文摘要：
One of the greatest challenges in cosmology today is to determine the nature of dark energy, the sourse of the observed present acceleration of the Universe. Besides the vacuum energy, various dark energy models have been suggested. The Friedmann - Robertson - Walker (FRW) spacetime plays an important role in modern cosmology. In particular, the most popular models of dark energy work in the FRW spacetime. In this work, a new class of integrable FRW cosmological models is presented. These models induced by the well-known Painlev$\acute{e}$ equations. Some nonintegrable FRW models are also considered. These last models are constructed with the help of Pinney, Schr$\ddot{o}$dinger and hypergeometric equations. Scalar field description and two-dimensional generalizations of some cosmological models are presented. Finally some integrable and nonintegrable $F(R)$ and $F(G)$ gravity models are constructed.
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