Entanglement in cosmology

We compute the evolution of the entanglement entropy for a massless field within a spherical region throughout the inflationary period and the subsequent era of radiation domination, starting from the Bunch-Davies vacuum. In order to focus on the entanglement of modes that are directly accessible to observations, we impose an ultraviolet cutoff set by the wavelength of the last mode that exited the horizon at the end of inflation. The transition of each mode towards a squeezed state upon horizon exit during inflation and the additional squeezing when radiation domination sets in enhance the entanglement entropy. Shortly after the transition to the radiation-dominated era, a volume term develops and becomes the leading contribution to the entropy at late times, as is common for systems lying in squeezed states. We estimate the magnitude of the entropy and discuss its interpretation in the light of the quantum to classical transition for modes exiting the horizon during inflation. Our results raise the possibility that the quantum nature of weakly interacting fields, such as gravitational waves resulting from tensor modes during inflation, may be detectable in today's universe. On the other hand, an observer with no knowledge of the degrees of freedom beyond the horizon would interpret the entropy as thermal. From this point of view, the reheating after inflation would be a result of quantum entanglement.