Entanglement generation from gravitationally produced massless vector particles during inflation

Abstract

We study the gravitational production of spectator massless vector particles in a single-field inflationary scenario, and the related entanglement generation across the Hubble horizon. Accordingly, we consider a quasi-de Sitter background evolution, with additional metric inhomogeneities induced by the inflaton quantum fluctuations. Afterwards, we compute the corresponding production amplitude and show that it depends only on the transverse polarizations, appearing \emph{de facto} gauge-invariant, consistently with our interpretation of the vector field as the electromagnetic one. We notice that particle wavelengths turn out to be small compared to the Hubble radius, thus favoring sub-Hubble production relative to super-Hubble one. In particular, highly energetic vector particles are preferentially produced and we show that polarization effects provide a significant contribution to this behavior. Moreover, the production of nearly collinear particle pairs appears as the most probable configuration, due to the background conformal invariance of the theory and the plane-wave (massless particle-like) nature of the metric perturbation. We thus specialize our treatment to super-Hubble scales, confirming their subdominant contribution to the number density of produced particles, albeit setting a corresponding lower bound on the reheating temperature. In this scheme, we explore superhorizon entanglement between sub- and super-Hubble field modes, computing the corresponding von Neumann entropy and discussing the effects of horizon crossing on the generation of primordial entanglement.

Figures (6)

• Figure 1: Amplitude containing the oscillating squared cardinal sine in comparison to that using the average in Eq. (\ref{['sincLorentzian']}). The functions are shown for a fixed value of $\overline{p}$ and different values of $x$, with respect to the independent variable $\overline{k}$. A log-lin scale is used.
• Figure 2: Density plot showing the magnitude of the integrand function of Eq. (\ref{['numberdensitycomputed']}) with respect to the rescaled momenta $\overline{k}$ and $\overline{p}$. Darker regions correspond to higher values of the function, indicating momenta at which particle production is most likely.
• Figure 3: Integrand function from Eq. (\ref{['numberdensitycomputed']}) as a function of the rescaled momentum $\overline{k}$, for different values of $\overline{p}$.
• Figure 4: Integrand function of Eq. (\ref{['numberdensitycomputedSH']}) with respect to the rescaled momentum $\overline{k}$ for different values of $\overline{p}$.
• Figure 5: Density plot showing the magnitude of the integrand function of Eq. (\ref{['entanglemententropyfinal']}) with respect to the rescaled momenta $\tilde{k}$ and $\tilde{p}$. Darker regions correspond to larger values of $\xi$, highlighting scales where sub- and super-Hubble modes result more entangled.