From Quantum to Classical in the Sky
  Inflation has by-far set itself as one of the prime ideas in the current
cosmological models that seemingly has an answer for every observed phenomenon
in cosmology. More importantly, it serves as a bridge between the early quantum
fluctuations and the present-day classical structures. Although the transition
from quantum to classical is still not completely understood till date, there
are two assumptions made in the inflationary paradigm in this regard:
  (i) the modes (metric perturbations or fluctuations) behave classically once
they are well outside the Hubble radius and,
  (ii) once they become classical they stay classical and hence can be
described by standard perturbation theory after they re-enter the Hubble
radius.
  We critically examine these assumptions for the tensor modes of (linear)
metric perturbations in a toy three stage universe with (i) inflation, (ii)
radiation-dominated and (iii) late-time accelerated phases. The
quantum-to-classical transition for these modes is evident from the evolution
of Wigner function in phase space and its peaking on the classical trajectory.
However, a better approach to quantify the degree of classicality and study its
evolution was given by Mahajan and Padmanabhan [1] using a classicality
parameter constructed from the parameters of the Wigner function. We study the
evolution of the classicality parameter across the three phases and it turns
out that the first assumption holds true, there is emergence of classicality on
Hubble exit, however the latter assumption of "once classical, always
classical" seems to lie on a shaky ground.
