Conservation of ζ with radiative corrections from heavy field
Conservation of ζ with radiative corrections from heavy field
复制标题
重场辐射校正的 ζ 守恒
DOI：
10.1088/1475-7516/2016/06/020
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Yuko Urakawa
中科院分区：
文献类型：
--
作者：
Takahiro Tanaka;Yuko Urakawa
在本文中，我们讨论了重标量场 χ 的辐射校正对曲率扰动 ζ 可能产生的影响。对 χ 进行积分，我们得出 ζ 的有效作用，其中包括重场 χ 的循环校正。当 χ 的质量远大于哈勃尺度 H 时，χ 的循环修正仅产生对有效作用的局部贡献，因此有效作用仅给出单场模型中 ζ 的作用，其中，众所周知，在哈勃穿越时间之后 ζ 在时间上守恒。同时，当 χ 的质量与 H 相当时，χ 的循环修正可以对有效作用做出非局部贡献。由于 χ 的非局部贡献，一般来说，即使经典背景轨迹仅由暴胀子的演化决定， z 也可能不守恒。在本文中，我们推导了在 χ 存在辐射修正的情况下 ze 时间守恒的条件。也就是说，我们证明，当作为微分同胚不变性的一部分的膨胀不变性在量子水平上得到保留时，大质量场χ的循环修正不会干扰超哈勃尺度上的δ的恒定演化。在本次讨论中，我们展示了膨胀不变性的 Ward-Takahashi 恒等式，它产生了大规模场 χ 的相关函数的一致性关系。
In this paper, we address a possible impact of radiative corrections from a heavy scalar field χ on the curvature perturbation ζ. Integrating out χ, we derive the effective action for ζ, which includes the loop corrections of the heavy field χ. When the mass of χ is much larger than the Hubble scale H, the loop corrections of χ only yield a local contribution to the effective action and hence the effective action simply gives an action for ζ in a single field model, where, as is widely known, ζ is conserved in time after the Hubble crossing time. Meanwhile, when the mass of χ is comparable to H, the loop corrections of χ can give a non-local contribution to the effective action. Because of the non-local contribution from χ, in general, ζ may not be conserved, even if the classical background trajectory is determined only by the evolution of the inflaton. In this paper, we derive the condition that ζ is conserved in time in the presence of the radiative corrections from χ. Namely, we show that when the dilatation invariance, which is a part of the diffeomorphism invariance, is preserved at the quantum level, the loop corrections of the massive field χ do not disturb the constant evolution of ζ at super Hubble scales. In this discussion, we show the Ward-Takahashi identity for the dilatation invariance, which yields a consistency relation for the correlation functions of the massive field χ.