Quantum Recoherence in Presence of Excited States in the Early Universe

TL;DR

This paper addresses the quantum-to-classical transition of primordial perturbations in a two-field inflationary setting where the adiabatic mode interacts with an entropic environment. It uses an open quantum systems framework with a derivative system–environment coupling $\lambda$ and parameterizes excited initial states of the adiabatic sector by Bogoliubov coefficients, notably reducing to the Bunch-Davies vacuum when $\alpha=0$. By solving the full Gaussian dynamics via the Transport Method and tracking purity $\gamma$ and Rényi-2 entropy $S_2$, the authors show that, for a massive environment, full recoherence is unique to the BD case; any initial excitation ($\alpha \neq 0$) induces a nonzero purity plateau (purity freezing) and prevents complete restoration of quantum coherence on super-Hubble scales. This sensitivity to initial conditions highlights the non-generic nature of recoherence in inflationary quantum-to-classical transitions and suggests potential observational consequences for residual quantum signatures in cosmological perturbations, motivating future work on $k$-dependent excitations and non-attractor backgrounds.

Abstract

We investigate the quantum-to-classical transition of primordial perturbations within a two-field inflationary framework where an adiabatic mode interacts with an entropic environment. In the case of a massive entropic environment, the attractor Bunch--Davies vacuum plays a special role: it is the only state that can undergo full recoherence, whereas all excited initial states exhibit persistent loss of purity. To characterize this behavior, we parameterize excited Gaussian initial states by their Bogoliubov coefficients and compute the purity and Rényi-2 entropy of the reduced adiabatic state as information-theoretic indicators of decoherence dynamics. We find that excited states display \emph{purity-freezing} at a non-zero plateau, where residual quantum correlations persist indefinitely, a qualitative departure from the complete recoherence observed for the Bunch--Davies vacuum. This sensitivity to initial conditions highlights the non-generic nature of full recoherence in the quantum-to-classical transition of inflationary perturbations.

Figures (7)

• Figure 1: Purity evolution $\gamma(N)$ for $\alpha\in\{-1,0,1\}$ and $m/H\in\{1,1.5,4\}$.
• Figure 2: Weak coupling $\lambda=0.05$, $m/H=1$. Rényi-2 $S_2$ stays below von Neumann $S_{\rm ent}$ and tracks its time dependence; for $\alpha=0$ both entropies grow monotonically after crossing, while for $\alpha=\pm 1$ a small super-horizon dip accompanies the transient purity rebound, followed by sustained entropy growth at late times.
• Figure 3: Weak coupling $\lambda=0.05$, $m/H=1.5$. The overall behavior mirrors the $m/H=1$ case with slightly reduced growth rates; excited initial states $\alpha=\pm 1$ again show a shallow early dip before converging to larger late-time entropy than the BD trajectory.
• Figure 4: Weak coupling $\lambda=0.05$, $m/H=4$. The BD vacuum ($\alpha=0$) displays the non-monotonic trend with an eventual decrease toward zero entropy, whereas $\alpha=\pm 1$ exhibits only a transient reduction, consistent with a purity freezing scenario.
• Figure 5: Strong coupling $\lambda=0.5$, $m/H=1$. Sub-horizon oscillations imprint small ripples before $N_{\rm cr}=0$; post-crossing, both $S_{\rm ent}$ and $S_2$ grow faster than in the weak-coupling case, with excited states showing a transient dip then sustained increase toward late times.