Fermionic influence (action) on inflationary fluctuations

TL;DR

This paper investigates how fermionic fields coupled to the inflaton during inflation can cause violations of scale invariance in the primordial power spectrum, revealing potential new physics in early universe cosmology.

Contribution

It derives an exact non-equilibrium effective action for inflaton fluctuations coupled to fermions, showing fermionic effects enhance super-Hubble fluctuations and violate scale invariance.

Findings

Fermionic couplings enhance the inflaton power spectrum on super-Hubble scales.

The power spectrum correction is renormalization group invariant.

A cancellation suggests a possible supersymmetric relation among fields.

Abstract

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.