arXiv 1602.056092016-02gr-qcastro-ph.COhep-phhep-th

费米对暴胀涨落的影响（action）

Fermionic influence (action) on inflationary fluctuations

Daniel Boyanovsky

备注：: matches published version. arXiv admin note: text overlap with arXiv:1511.06649
发表信息：: Phys. Rev. D 93, 083507 (2016)
DOI：: 10.1103/PhysRevD.93.083507

摘要：

出于明显的持续大尺度异常的CMB，我们研究的影响，费米自由度的暴胀波动的动力学作为一个可能的来源违反（近）尺度不变性的宇宙尺度。本文研究了de Sitter时空中Dirac场和Majorana场的类暴胀子汤川相互作用标量场（$Y_{D,M}$）对轻\emph{fermionic}自由度的非平衡有效作用量.有效的行动导致朗之万运动方程的暴胀子类场的波动，自能修正和随机高斯噪声。我们解决了朗之万方程的超哈勃极限实施的动力学重整化群重正化。对于几乎无质量的暴胀子，其超哈勃涨落的功率谱是\emph{enhanced}，对于$N_D$狄拉克费米子和$N_M$马约拉纳费米子，$\mathcal{P}(k;η) = (\frac{H}{2π})^2\,e^{γ_t[-kη] }$和$γ_t[-kη] = \frac{1}{6π^2} \Big[\sum_{i=1}^{N_D}{Y^2_{i,D}}+2\sum_{j=1}^{N_M}{Y^2_{j,M}}\Big]\,\Big\{\ln^2[-kη]-2 \ln[-kη]\ln[ -kη_0] \Big\} $，$η_0$是暴胀子质量消失时的重整化标度。全功率谱是重整化群不变的。这些修正的超级哈勃功率谱需要违反尺度不变性的耦合到费米子场的结果。在大量费米子场的极限下，有效作用量为\emph{exact}.从费米自由度的增强和从光标量自由度的抑制之间的抵消\emph{conformally coupled to gravity}建议在这些领域之间的微调\emph{supersymmetry}的可能性。

英文摘要：

Motivated by apparent persistent large scale anomalies in the CMB we study the influence of fermionic degrees of freedom on the dynamics of inflaton fluctuations as a possible source of violations of (nearly) scale invariance on cosmological scales. We obtain the non-equilibrium effective action of an inflaton-like scalar field with Yukawa interactions ($Y_{D,M}$) to light \emph{fermionic} degrees of freedom both for Dirac and Majorana fields in de Sitter space-time. The effective action leads to Langevin equations of motion for the fluctuations of the inflaton-like field, with self-energy corrections and a stochastic gaussian noise. We solve the Langevin equation in the super-Hubble limit implementing a dynamical renormalization group resummation. For a nearly massless inflaton its power spectrum of super Hubble fluctuations is \emph{enhanced}, $\mathcal{P}(k;η) = (\frac{H}{2π})^2\,e^{γ_t[-kη] }$ with $γ_t[-kη] = \frac{1}{6π^2} \Big[\sum_{i=1}^{N_D}{Y^2_{i,D}}+2\sum_{j=1}^{N_M}{Y^2_{j,M}}\Big]\,\Big\{\ln^2[-kη]-2 \ln[-kη]\ln[ -kη_0] \Big\} $ for $N_D$ Dirac and $N_M$ Majorana fermions, and $η_0$ is the renormalization scale at which the inflaton mass vanishes. The full power spectrum is shown to be renormalization group invariant. These corrections to the super-Hubble power spectrum entail a violation of scale invariance as a consequence of the coupling to the fermionic fields. The effective action is argued to be \emph{exact} in a limit of large number of fermionic fields. A cancellation between the enhancement from fermionic degrees of freedom and suppression from light scalar degrees of freedom \emph{conformally coupled to gravity} suggests the possibility of a finely tuned \emph{supersymmetry} among these fields.

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