  We show that the entropy of cosmological perturbations originating as quantum
vacuum fluctuations in the very early universe, including the contribution of
the leading nonlinear interactions, can be viewed as momentum space
entanglement entropy between sub- and super-Hubble modes. The interactions
between these modes causes decoherence of the super-Hubble fluctuations which,
in turn, leads to a non-vanishing entropy of the reduced density matrix
corresponding to the super-Hubble inhomogeneities. In particular, applying this
to inflationary cosmology reveals that the entanglement entropy produced by
leading order nonlinearities dominates over that coming from the squeezing of
the vacuum state unless inflation lasts for a very short period. Furthermore,
demanding that this entanglement entropy be smaller than the thermal entropy at
the beginning of the radiation phase of standard cosmology leads to an upper
bound on the duration of inflation which is similar to what is obtained from
the Trans-Planckian Censorship Conjecture.
