  We discuss the primordial spectrum of a massless and minimally coupled scalar
field, produced during the initial anisotropic epoch before the onset of
inflation. We consider two models of the anisotropic cosmology, the (planar)
Kasner de Sitter solution (Bianchi I) and the Taub-NUT de Sitter solution
(Bianchi IX), where the 3-space geometry is initially anisotropic, followed by
the de Sitter phase due to the presence of a positive cosmological constant. We
discuss the behavior of a quantized, massless and minimally coupled scalar
field in the anisotropic stage. We focus on the quantization procedure and
evolution in the pre-inflationary anisotropic background. The initial condition
is set by the requirement that the scalar field is initially in an adiabatic
state. In our case, such a vacuum state exists only for limited solutions of
the anisotropic Universe, whose spacetime structure is regular in the initial
times. In this paper, we call our adiabatic vacuum state the anisotropic
vacuum. In the Kasner de Sitter model, for one branch of planar solutions there
is an anisotropic vacuum unless $k_3\neq 0$, where $k_3$ is the comoving
momentum along the third direction, while in the other branch there is no
anisotropic vacuum state. In the first branch, for the moderate modes, $k_3\sim
k$, where $k$ is the total comoving momentum, the scalar power spectrum has an
oscillatory behavior and its direction dependence is suppressed. For the planar
modes, $k_3\ll k$, in contrast, the direction dependence becomes more
important, because of the amplification of the scalar amplitude during this
interval of the violation of WKB approximation in the initial anisotropic
stage. The qualitative behaviors in the Taub-NUT de Sitter models are very
similar to the case of the first branch of the planar Kasner de Sitter model.
