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 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 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.
