Imprint of entanglement entropy in the power spectrum of inflationary fluctuations

TL;DR

This paper investigates how entanglement entropy generated by fermion couplings during inflation affects the inflaton's power spectrum, revealing scale invariance violations linked to quantum entanglement.

Contribution

It introduces a model connecting entanglement entropy growth with modifications in the inflationary power spectrum due to fermion couplings during inflation.

Findings

Entanglement entropy grows during inflation due to fermion pair production.

Power spectrum exhibits scale invariance violations correlated with entanglement entropy.

Analytical expression for the entanglement entropy and its impact on the power spectrum is provided.

Abstract

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.