报告题目:Analytical calculation of 2nd-order cosmological perturbations

报告人：王博 副研究员（中国科学技术大学）

报告时间：2023年6月13日（周二）上午 10:00-12:00

报告地点：浙江工业大学理学楼A 二楼师生活动中心

摘 要 (Abstract): With the improvement of cosmological observation precision, nonlinear perturbations have become necessary to understand the cosmological phenomenons. In the framework of general relativity, we analytically study the perturbations of the metric and of the scalar field for a power-law inflation, of the density, pressure and velocity of a relativistic fluid model during the radiation-dominated stage, of the density of a dust model during the matter-dominated stage, in synchronous coordinates. We analyze the structure of the 1st- and 2nd-order perturbed Einstein equations and give the 1st- and 2nd-order solutions. The 2nd-order perturbed Einstein equations are similar in structure to the 1st-order ones, but various products of the 1st-order perturbations occur as the effective source. We perform the residual gauge transformations between synchronous coordinates up to the 2nd-order, and present the gauge modes of 1st- and 2nd-order perturbations. During inflation both the scalar metric perturbation and the perturbed scalar field are waves propagating at the speed of light, analogous to the tensor perturbation, and different from those in the dust and relativistic fluid models in which only tensor perturbation propagates at the speed of light and is regarded as gravitational waves but scalars and vectors do not. The 1st-order vector perturbation during inflation is not a wave and decreases with expansion, but the 2nd order vector perturbation is a wave since it consists of products of the 1st-order scalar perturbations. This causes the 1st-order vector modes to vanish as the universe evolves but the 2nd-order vector modes present inevitably. For the inflation stage, we investigate four gauge invariant scalar perturbations and use the zero-point energy of the scalar field in the vacuum to determine the initial conditions and yield corresponding primordial spectra. For the raditation- and matter-dominated stages, we keep the integration constants in the 2nd-order solutions which shall be used to connect with the inflation stage solutions and to achieve a whole evolution picture of the 2nd order in our future plan.

报告人简介(Bio): 王博，男，中国科学技术大学特任副研究员。主要从事宇宙学非线性扰动的解析计算及其可观测效应分析、引力波的理论和观测相关的研究。共发表SCI论文13篇，其中第一/通讯作者发表10篇，包括以共同通讯作者发表PRL一篇、以第一作者兼通讯作者发表ApJS一篇。主持过国家自然科学基金委员会青年科学基金、中国博士后科学基金面上资助、中国科学技术大学青年创新基金，并作为骨干成员兼科研助理参与了中国科技部国家重点研发计划“引力波探测”重点专项项目。入选了2019年“中科院特别研究助理资助项目”，并获得2019年和2022年中国科学技术大学“墨子杰出青年特资津贴”支持。

邀请人：朱涛 教授