  I study the "general" case that arises in the Extended Effective Field Theory
of Inflation (gEEFToI), in which the coefficients of the sixth order polynomial
dispersion relation depend on the physical wavelength of the fluctuation mode,
hence they are time-dependent. At arbitrarily short wavelengths the unitarity
is lost for each mode. Depending on the values of the gEEFToI parameters in the
unitary gauge action, two scenarios can arise: in one, the coefficients of the
polynomial become singular, flip signs at some physical wavelength and
asymptote to a constant value as the wavelength of the mode is stretched to
infinity. Starting from the WKB vacuum, the two-point function is essentially
singular in the infinite IR limit. In the other case, the coefficients of the
dispersion relation evolve monotonically from zero to a constant value in the
infinite IR. In order to have a finite power spectrum starting from the vacuum
in this case, the mode function has to be an eigensolution of the Confluent
Heun (CH) equation, which leads to a very confined parameter space for gEEFToI.
Finally, I look at a solution of the CH equation which is regular in the
infinite IR limit and yields a finite power spectrum in either scenario. I
demonstrate that this solution asymptotes to an excited state in past infinity
in both cases. The result is interpreted in the light of the loss of unitarity
for very small wavelengths. The outcome of such a non-unitary phase evolution
should prepare each mode in the excited initial state that yields a finite
two-point function for all the parameter space. This will be constraining of
the new physics that UV completes such scenarios.
