# Fermionic influence (action) on inflationary fluctuations [CL]

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}, $\mathcal{P}(k;\eta) = (\frac{H}{2\pi})^2\,e^{\gamma_t[-k\eta] }$ with $\gamma_t[-k\eta] = \frac{1}{6\pi^2} \Big[\sum_{i=1}^{N_D}{Y^2_{i,D}}+2\sum_{j=1}^{N_M}{Y^2_{j,M}}\Big]\,\Big\{\ln^2[-k\eta]-2 \ln[-k\eta]\ln[ -k\eta_0] \Big\}$ for $N_D$ Dirac and $N_M$ Majorana fermions, and $\eta_0$ 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.

D. Boyanovsky
Fri, 19 Feb 16
43/50

Comments: 34 pages, 1 fig. arXiv admin note: text overlap with arXiv:1511.06649