We investigate the quantum evolution of the universe in the presence of two types of dark energies. First, we consider the phantom class ($\omega <-1$) which would be responsible for a super-accelerated cosmic expansion, and then we apply the procedure to an ordinary $\Lambda >0$ vacuum ($\omega =-1$). This is done by analytically solving the Wheeler–DeWitt equation with ordering term (WdW) in the cosmology of Friedmann–Robertson–Walker. In this paper, we find exact solutions in the scale factor $a$ and the ordering parameter $q$. For $q=1$ it is shown that the universe has a high probability of evolving from a big bang singularity. On the other hand, for $q=0$ the solution indicates that an initial singularity is unlikely. Instead, the universe has maximal probability of starting with a finite well-defined size which we compute explicitly at primordial times. We also study the time evolution of the scale factor by means of the Hamilton–Jacobi equation and show that an ultimate big rip singularity emerges explicitly from our solutions. The phantom scenario thus predicts a dramatic end in which the universe would reach an infinite scale factor in a finite cosmological time as pointed by Caldwell et al. in a classical setup (Caldwell et al., 2003). Finally, we solve the WdW equation with ordinary constant dark energy and show that in this case the universe does not rip apart in a finite era.

我们研究存在两种暗能量时宇宙的量子演化。首先，我们考虑幻影类（$\omega <-\mathrm{1个}$），这将导致超加速宇宙膨胀，然后我们将该程序应用于普通 $\Lambda >0$ 真空（$\omega =-\mathrm{1个}$）。这是通过在Friedmann-Robertson-Walker宇宙学中用有序项（WdW）解析Wheeler-DeWitt方程来完成的。在本文中，我们找到了比例因子的精确解$\mathrm{一种}$ 和订购参数 $q$。对于$q=\mathrm{1个}$结果表明，宇宙具有很大的爆炸性。另一方面，对于$q=0$该解决方案表明初始奇点不太可能。相反，宇宙具有从有限的明确定义的大小开始的最大概率，我们在原始时间明确地计算了大小。我们还通过汉密尔顿-雅各比方程研究了比例因子的时间演化，并证明了最终的大裂点奇点从我们的解决方案中显露出来。幻像场景因此预测了一个戏剧性的结局，即宇宙将在有限的宇宙学时间内达到无限的比例因子，正如Caldwell等人所指出的那样。以经典的方式（Caldwell等，2003）。最后，我们用普通的恒定暗能量求解WdW方程，并表明在这种情况下，宇宙不会在有限的时代分裂。