Impact of quantum entanglement induced by magnetic fields on primordial gravitational waves

There exists observational evidence to believe in the existence of primordial magnetic fields generated during inflation. We study primordial gravitational waves (PGWs) during inflation in the presence of magnetic fields sustained by a gauge kinetic coupling. In the model, not only gravitons as excitations of PGWs, but also photons as excitations of electromagnetic fields are highly squeezed. They become entangled with each other through graviton to photon conversion and vice versa. We derive the reduced density matrix for the gravitons and calculate their entanglement entropy. It turns out that the state of the gravitons is not a squeezed state but a mixed state. Although witnessing such an entanglement is not feasible at present, it would be an important experimental challenge.

Automated summary

There is observational evidence for the existence of primordial magnetic fields generated during inflation. We investigate primordial gravitational waves during inflation in the presence of magnetic fields sustained by a gauge kinetic coupling. In this model, both gravitons as excitations of primordial gravitational waves, and photons as excitations of electromagnetic fields are strongly squeezed, and become entangled through graviton to photon conversion. We calculate the entanglement entropy of the gravitons and find that their state is a mixed state rather than a squeezed state.