标题： 暴胀宇宙学中的能量密度涨落 显示英文标题

标题： Energy Density Fluctuations in Inflationary Cosmology

摘要： 我们分析由期望值为零的标量场$\Phi$引起的能量密度涨落，$\langle\Phi\rangle=0$，它们除了暴胀场之外还存在。为了简便，我们取$\Phi$为非相互作用且与引力最小耦合。我们使用正规排序来定义重整化后的能量密度算符$\rho$，并且我们证明任何正规排序对于$\rho$的关联函数都给出相同的结果。我们首先考虑无质量场，并推导单个模式$\vk$的能量涨落，能量密度的两点关联函数、功率谱以及平滑能量密度的方差，$\ddR$。研究了单个模式中能量涨落的质量效应。所有考虑的量在第二次视界穿越时（Harrison-Zel'dovich型）对于无质量场和不稳定的质量场都是尺度不变的。 相对涨落的大小$\de\rho/\rt$在无质量情况下为$(\Hi/\Mp)^2$的量级，其中$\Hi$是暴胀期间的哈勃常数。 对于质量为$m_\Phi\ll\Hi$的不稳定场，其衰变率为$\Gamma_\Phi$，其大小会增强一个因子$\sqrt{m_\Phi/\Gamma_\Phi}$。 最后，给出了在无质量情况下样本中平均能量密度的宇宙方差预测。 显示英文摘要

摘要： We analyze the energy density fluctuations contributed by scalar fields $\Phi$ with vanishing expectation values, $\langle\Phi\rangle=0$, which are present in addition to the inflaton field. For simplicity we take $\Phi$ to be non--interacting and minimally coupled to gravity. We use normal ordering to define the renormalized energy density operator $\rho$, and we show that any normal ordering gives the same result for correlation functions of $\rho$. We first consider massless fields and derive the energy fluctuations in a single mode $\vk$, the two--point correlation function of the energy density, the power spectrum, and the variance of the smeared energy density, $\ddR$. Mass effects are investigated for energy fluctuations in single modes. All quantities considered are scale invariant at the second horizon crossing (Harrison--Zel'dovich type) for massless and for unstable massive fields. The magnitude of the relative fluctuations $\de\rho/\rt$ is of order $(\Hi/\Mp)^2$ in the massless case, where $\Hi$ is the Hubble constant during inflation. For an unstable field of mass $m_\Phi\ll\Hi$ with a decay rate $\Gamma_\Phi$ the magnitude is enhanced by a factor $\sqrt{m_\Phi/\Gamma_\Phi}$. Finally, the prediction for the cosmic variance of the average energy density in a sample is given in the massless case.