Imprint of entanglement entropy in the power spectrum of inflationary
  fluctuations
  If the inflaton couples to other degrees of freedom that populate the
post-inflationary stage, such coupling modifies the dynamics of the inflaton
\emph{during} inflation. We consider light fermions Yukawa coupled to the
inflaton as "unobserved" degrees of freedom integrated out of the total density
matrix. Tracing out these degrees of freedom yields a \emph{mixed} density
matrix whose time evolution is described by an effective field theory. We show
that the coupling leads to profuse fermion pair production for super-Hubble
inflaton fluctuations which lead to the \emph{growth of entanglement entropy
during inflation}. The power spectrum of inflaton fluctuations features scale
invariance violations $\mathcal{P}(k) = \mathcal{P}_0(k)\,\,\exp\{8\,\xi_k\}$
with corrections to the \emph{index and its running directly correlated with
the entanglement entropy}: $S_{vN} = - \sum_{k} \Big[ \ln(1-\xi_k) +
\frac{\xi_k\,\ln(\xi_k)}{1-\xi_k} \Big]$. For super-Hubble fluctuations we find
$\xi_k = -\frac{Y^2}{48\pi^2}\Big\{2\,N_T\,\ln(k/k_f) + \ln^2(k/k_f)\Big\}$
with $Y$ the Yukawa coupling, $N_T$ the total number of e-folds during
inflation, and $k_f$ a "pivot" scale corresponding to the mode that crosses the
Hubble radius at the end of inflation.
