Entanglement time in the primordial universe

We investigate the behavior of the entanglement entropy of space in the primordial phase of the universe before the beginning of the cosmic inflation. We argue that in this phase the entanglement entropy of a region of space grows from a zero-law to an area-law. This behavior provides a quantum version of the classical Belinsky-Khalatnikov-Lifshitz (BKL) conjecture that spatially separated points decouple in the approach to a cosmological singularity. We show that the relational growth of the entanglement entropy with the scale factor provides a new statistical notion of arrow of time in quantum gravity. The growth of entanglement in the pre-inflationary phase provides a mechanism for the production of the quantum correlations present at the beginning of inflation and imprinted in the CMB sky.