具有宇宙学常数和理想流体状态方程的FRW宇宙的分类$p = wρ$
Classification of the FRW universe with a cosmological constant and a perfect fluid of the equation of state $p = wρ$
摘要：
系统地研究了耦合宇宙学常数$Λ$和具有状态方程$p=wρ$的理想流体的Friedmann-Robertson-Walker（FRW）宇宙的演化，其中$p$和$ρ$分别表示流体的压力和能量密度，$w$是任意实常数.根据$w,\; Λ$的具体值和三维空间的曲率$k$，我们将所有的解分成不同的情况。在每一种情况下的演化的主要属性的详细信息，包括减速和/或加速的周期，以及大爆炸，大紧缩，和大撕裂奇点的存在。在某些情况下，标准教科书中出现的分类和解释错误已得到纠正。
英文摘要：
We systematically study the evolution of the Friedmann-Robertson-Walker (FRW) universe coupled with a cosmological constant $Λ$ and a perfect fluid that has the equation of state $p=wρ$, where $p$ and $ρ$ denote, respectively, the pressure and energy density of the fluid, and $w$ is an arbitrary real constant. Depending on the specific values of $w,\; Λ$, and the curvature $k$ of 3-dimensional space, we separate all of the solutions into various cases. In each case the main properties of the evolution are given in detail, including the periods of deceleration and/or acceleration, and the existence of big bang, big crunch, and big rip singularities. In some cases, errors in classification and interpretation appearing in standard textbooks have been corrected.
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