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arXiv 1004.0882gr-qcastro-ph.COhep-th
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暴胀扰动的路径积分

Path Integral for Inflationary Perturbations

Tomislav Prokopec, Gerasimos Rigopoulos

摘要:

用路径积分描述了单场暴胀中宇宙学扰动的量子理论。从一个规范公式出发,我们展示了如何从众所周知的规范不变的标量和张量扰动的二次作用量中得到自由传播子,并确定了任意阶的相互作用。这种方法不需要显式的解决方案的能量和动量约束,一个新的功能,简化了相互作用顶点的确定。规范条件的限制和必要的强加反映在作用量中各种对易和反对易辅助场的出现上。这些辅助场不传播物理自由度,但需要包括在图解展开中的内部线和环路中。为了说明的形式主义,我们讨论了树级的3点和4点函数的暴胀子扰动,再现已经得到的结果,在目前的文献中使用的方法。循环计算留待以后处理。

英文摘要:

The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known gauge-invariant quadratic action for scalar and tensor perturbations, and determine the interactions to arbitrary order. This approach does not require the explicit solution of the energy and momentum constraints, a novel feature which simplifies the determination of the interaction vertices. The constraints and the necessary imposition of gauge conditions is reflected in the appearance of various commuting and anti-commuting auxiliary fields in the action. These auxiliary fields are not propagating physical degrees of freedom but need to be included in internal lines and loops in a diagrammatic expansion. To illustrate the formalism we discuss the tree-level 3-point and 4-point functions of the inflaton perturbations, reproducing the results already obtained by the methods used in the current literature. Loop calculations are left for future work.

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