Quantum entanglement and non-Gaussianity in the primordial Universe

We propose a new method to investigate signatures of a quantum gravity phase in the primordial state of cosmological perturbations. We formulate and study a quantum model of a perturbed Friedmann-Lema\^{\i}tre-Robertson-Walker universe beyond a tensor-product Born-Oppenheimer-like factorization, that is, without restricting the wave function of the universe to the product of the background and perturbation wave functions. We show that the quantum dynamics generically does not preserve the product form of the universe's wave function, which spontaneously evolves into a more general entangled state. Upon expanding this state in a suitable basis of background wave functions and setting Gaussian initial conditions for the perturbations, we numerically find that each of these wave functions becomes associated with a non-Gaussian state of an inhomogeneous perturbation.