  We consider the possibility to solve the issues of the phantom field
cosmology by means of the PT-symmetric quantum theory. The Born-Oppenheimer
approximation is applied to the Wheeler-DeWitt equation to study the
inhomogeneous fluctuations over the homogeneous minisuperspace. The evolution
of the longitudinal inhomogeneous modes in WKB-time is described using a
time-dependent pseudo-Hermitian effective Hamiltonian.
