Fermionic influence (action) on inflationary fluctuations
  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.
