  There exists the "entropy problem" of the early universe, that is, why did
the universe begin with an extremely low entropy and how did it evolve into
such high entropy at late times? It has been long believed that inflation
cannot be the solution since it requires an extremely low entropy to ever
occur. However, we point out that since the inflation is always accompanied
with a horizon, the correct probability of inflation is associated with the
quantum entanglement entropy, which should in principle be larger than what
considered previously. This motivates us to reexamine the issue by computing
the evolution of the cosmological entanglement entropy in the early universe.
We invoke a toy model of nonlinear generalized Chaplygin gas (GCG), which has
the advantage of providing a smooth and unitary transition between the
inflation epoch and the radiation dominant era. We found that soon after the
onset of the inflation, the total entanglement entropy rapidly decreases to a
minimum, and it rises monotonically afterwards throughout the remainder of the
inflation and the radiation epochs. This indicates that the universe does not
need to begin with an extremely low entropy; its smallness can be naturally
induced by the dynamics of inflation itself. We believe that our computation
largely captures the essential feature of entropy evolution and can provide us
insights beyond the toy model.
