Study of a quantum inhomogeneous universe

为了理解宇宙非均匀结构的量子起源，本项目研究了时空度规的量子涨落与物质场的量子涨落之间的关系。(1)指数膨胀宇宙中的量子涨落研究表明，指数膨胀模型中的红外量子涨落比指数膨胀模型中的量子涨落更不稳定。利用这种不稳定性，我们发现，在一个含有主子的统一模型中，重子谱正好是结构形成的最小等温情景所需要的。此外，发现概率分布在小尺度上是高度非高斯的，但在大尺度上是高斯分布。(2)早期宇宙中的量子隧穿要理解宇宙中的量子隧穿，分析耗散环境的影响以及了解引力的作用是很重要的。作为第一步，给出了具有耗散的量子隧穿的正则公式，并证明了耗散相互作用不一定抑制隧穿速率。然后，研究了在引力作用下的假真空衰变，发现引力模的存在显著改变了先前的幼稚图景。

In order to understand the quantum origin of inhomogeneous structures of the universe, the relation between quantum fluctuations of the spacetime metric and those of matter fields has been investigated in this project. (1)Quantum fluctuations in the power-law inflationary universe It was shown that the infrared quantum fluctuations in a power-law inflation model are more unstable than those in exponential inflation. Using this instability, the baryon spectrum in a unified model with majoron is found to be exactly what one needs for the minimal isocurvature scenario of the structure formation. Further, the probability distribution is found to be highly non-Gaussian on small scales but is Gaussian on large scales. (2)Quantum tunneling in the early universe To understand quantum tunneling in the universe, it is important to analyze the effect of dissipative environment, as well as to know the role of gravity. As a first step, a canonical formulation of quantum tunneling with dissipation was given and it was shown that dissipative interactions may not necessarily suppress the tunneling rate. Then, false vacuum decay under the presence of gravity was investigated and it was found that the existence of gravitational modes changes the previous naive picture significantly.