  We investigate the possibility that the inflationary period in the early
universe was preceded by a primordial stage of strong anisotropy. In particular
we focus on the simplest model of this kind, where the spacetime is described
by a non-singular Kasner solution that quickly evolves into an isotropic de
Sitter space, the so-called Kasner-de Sitter solution. The initial Big Bang
singularity is replaced, in this case, by a horizon. We show that the extension
of this metric to the region behind the horizon contains a timelike singularity
which will be visible by cosmological observers. This makes it impossible to
have a reliable prediction of the quantum state of the cosmological
perturbations in the region of interest. In this paper we consider the
possibility that this Kasner-de Sitter universe is obtained as a result of a
quantum tunneling process effectively substituting the region behind the
horizon by an anisotropic parent vacuum state, namely a $1+1$ dimensional
spacetime compactified over an internal flat torus, $T_2$, which we take it to
be of the form ${de Sitter}_2 \times T_2$ or ${Minkowski}_2 \times T_2$. As a
first approximation to understand the effects of this anisotropic initial
state, we compute the power spectrum of a massless scalar field in these
backgrounds. In both cases, the spectrum converges at small scales to the
isotropic scale invariant form and only present important deviations from it at
the largest possible scales. We find that the decompactification scenario from
$M_2 \times T_2$ leads to a suppressed and slightly anisotropic power spectrum
at large scales which could be related to some of the anomalies present in the
current CMB data. On the other hand, the spectrum of the universe with a $dS_2
\times T_2$ parent vacuum presents an enhancement in power at large scales not
consistent with observations.
