What initial condition of inflation would suppress the large-scale CMB
  spectrum?
  There is an apparent power deficit relative to the $\Lambda$CDM prediction of
the CMB spectrum at large scales, which, though not yet statistically
significant, persists from WMAP to Planck data. Proposals that invoke some form
of initial condition for the inflation have been made to address this apparent
power suppression, albeit with conflicting conclusions. By studying the
curvature perturbations of a scalar field in the FLRW universe parameterized by
the equation of state parameter $w$, we find that the large-scale spectrum at
the end of inflation reflects the super-horizon spectrum of the initial state.
The large-scale spectrum is suppressed if the universe begins with the
adiabatic vacuum in a super-inflation ($w < -1$) or positive-pressure ($w > 0$)
era. In the latter case, there is however no causal mechanism to establish the
initial adiabatic vacuum. On the other hand, as long as the universe begins
with the adiabatic vacuum in an era with $-1 < w < 0$, even if there exists an
intermediate positive-pressure era, the large-scale spectrum would be enhanced
rather than suppressed. We further calculate the spectrum of a two-stage
inflation model with a two-field potential and show that the result agrees with
that obtained from the ad hoc single-field analysis.
