This thesis investigates the entanglement entropy of cosmological perturbations in expanding FLRW universes dominated by either radiation or matter. Motivated by the idea that spacetime geometry may emerge from quantum informational principles, we study the entanglement entropy between long- (super-Hubble) and short-wavelength (sub-Hubble) modes arising from cubic gravitational interactions. We partition the Hilbert space of perturbations into two subsystems: the system, consisting of super-Hubble modes, and the bath, consisting of sub-Hubble modes, and compute the entanglement entropy of the super-Hubble sector after tracing out the short-wavelength degrees of freedom. Starting from the Einstein–Hilbert action minimally coupled to a canonical scalar field, we derive the quadratic and cubic actions for curvature perturbations in the comoving gauge and identify the interaction terms most relevant on super-Hubble scales. Using these interactions, we evaluate the leading-order contribution to the system’s entanglement entropy. The resulting expressions exhibit both ultraviolet and infrared divergences, which reflect the regulator dependence of the effective field theory; the UV part is expected to be resolved in a UV-complete description, while the IR part arises from the use of an idealized free-field description. After UV-IR regularization, a finite, physically meaningful contribution remains. This regularized entanglement entropy decays as Sent,reg ~ a-7 in the radiation era and Sent,reg ~ a-9/2 in the matter era, reflecting a gradual purification of the global quantum state as modes re-enter the Hubble radius. The results quantify how the cosmological expansion in an FLRW background dynamically modulates quantum correlations between modes across the Hubble scale, leading to a monotonic decay of the entanglement entropy over time.
Emilie Desrochers Karlsson (Wed,) studied this question.