  We analyze a quantized toy model of a universe undergoing eternal inflation
using a quantum-field-theoretical formulation of the Wheeler-DeWitt equation.
This so-called third quantization method leads to the picture that the
eternally inflating universe is converted to a multiverse in which
sub-universes are created and exhibit a distinctive phase in their evolution
before reaching an asymptotic de Sitter phase. From the perspective of one of
these sub-universes, we can thus analyze the pre-inflationary phase that arises
naturally. Assuming that our observable universe is represented by one of those
sub-universes, we calculate how this pre-inflationary phase influences the
power spectrum of the cosmic microwave background (CMB) anisotropies and
analyze whether it can explain the observed discrepancy of the power spectrum
on large scales, i.e. the quadrupole issue in the CMB. While the answer to this
question is negative in the specific model analyzed here, we point out a
possible resolution of this issue.
