标题： 具有精确量子经典对应的弹跳和滑行宇宙 显示英文标题

标题： Bouncing and coasting universe with exact quantum-classical correspondence

摘要： 当宇宙的膨胀尺度因子写成$ a(t)\equiv Ae^{\alpha(t)}$，其中$A$为某个实常数，$\alpha(t)$为一个实函数时，引力作用$I_G$以与物质作用$I_M$相同的形式出现，对于具有特定尺度因子依赖势的均匀各向同性标量场而言。 我们观察到，通过对这个$I_G$中的拉格朗日函数进行解析延拓到$\alpha$的复平面，可以获得描述可行宇宙学模型的总作用量的两个部分的项。 该解给出一个反弹和匀速宇宙，它首先收缩然后线性膨胀，在两者之间有一个平滑的反弹。 这种反弹被称为托尔曼虫洞，这是由于在解中自然出现的类似卡西米尔的负能量。 在一种新的量子宇宙学方法中，我们使用算子方法对上述模型进行正则量子化，并表明它可以避免传统形式主义中的算子顺序歧义。 这导致了一个宇宙的量子波方程，求解该方程得到有趣的结果，即宇宙处于具有非零能量的基态。 该解不同于 Wheeler-DeWitt 波函数，并在所有时期都具有精确的量子经典对应关系。 显示英文摘要

摘要： When the scale factor of expansion of the universe is written as $ a(t)\equiv Ae^{\alpha(t)}$, with $A$ as some real constant and $\alpha(t)$ a real function, the gravitational action $I_G$ appears in the same form as the matter action $I_M$ for a homogeneous and isotropic scalar field with a specific scale factor-dependent potential. We observe that by making analytic continuation of the Lagrangian function in this $I_G$ to the complex plane of $\alpha$, one can obtain terms corresponding to both parts of a total action that describes a viable cosmological model. The solution gives a bouncing and coasting universe, which first contracts and then expands linearly, with a smooth bounce in between them. Such a bounce, called a Tolman wormhole, is due to a Casimir-like negative energy that appears naturally in the solution. In a novel approach to quantum cosmology, we perform canonical quantization of the above model using the operator method and show that it can circumvent the operator ordering ambiguity in the conventional formalism. It leads to a quantum wave equation for the universe, solving which we get the interesting result that the universe is in a ground state with nonzero energy. This solution is different from the Wheeler-DeWitt wave function and possesses exact quantum-classical correspondence during all epochs.