arXiv 2007.009042020-07gr-qcastro-ph.COhep-th

存在引力粒子产生时宇宙学度规扰动的性质

The nature of cosmological metric perturbations in presence of gravitational particle production

Kaushik Bhattacharya, Anirban Chatterjee, Saddam Hussain

备注：: 24 pages, 6 figures. The title and abstract of the paper is modified. Some errors in previous version are corrected and some new material is added in this version. This version is accepted for publication in General Relativity and Gravitation (GERG)

摘要：

本文试图回答这样一个问题：在辐射存在下的deSitter相是否是早期宇宙标准暴胀范式的竞争者？这种德西特相可以存在于发生引力粒子产生的宇宙学模型中。为了解决这个问题，在德西特阶段的辐射存在的度量扰动必须是已知的。本文计算了度规扰动的演化。可以看出，标量和矢量扰动的演变与标准的暴胀模型有很大的不同。这些差异是由颗粒产生机制引起的。标量扰动功率谱在小尺度上呈指数增长。然而，人们不能唯一地指定的规模，在这个指数增长开始，因为依赖于初始扰动值的功率谱。初始扰动开始的时间片是任意的。初始时间片的任意性与当前模型中对扰动设置初始条件的问题有关。本文对充满辐射的de Sitter空间中的矢量和张量扰动作了简要的讨论。可以看出，在本模型中的微扰模式的量子化是相当困难的。必须修改本模型，以提供一个一致的方案的量子化的微扰模式。

英文摘要：

The present paper tries to answer the question: Can a de Sitter phase in presence of radiation be a competitor of the standard inflationary paradigm for the early universe? This kind of a de Sitter phase can exist in cosmological models where gravitational particle production takes place. To address the issue the metric perturbations in the de Sitter phase in presence of radiation must be known. The evolution of metric perturbations are explicitly calculated in the paper. It is seen that the evolution of scalar and vector perturbations are considerably different from standard inflationary models. These differences arise due to the particle production mechanism. The scalar perturbation power spectrum grows exponentially at small length scales. However, one cannot uniquely specify the scale at which this exponential growth starts because of the dependence of the power spectrum on the initial perturbation value. The time slice on which the initial perturbation starts is arbitrary. The arbitrariness of the initial time slice is related to the problem of setting the initial condition on the perturbations in the present model. The paper briefly opines on vector and tensor perturbations in the de Sitter space filled with radiation. It is seen that quantization of the perturbation modes in the present model is considerably difficult. One has to modify the present model to provide a consistent scheme of quantization of the perturbation modes.

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