  We investigate, in the transverse traceless (TT) gauge, the generation of the
relic background of gravitational waves, generated during an early inflationary
stage, on the framework of a large-scale repulsive gravity model. We calculate
the spectrum of the tensor metric fluctuations of an effective 4D
Schwarzschild-de-Sitter metric, which is obtained after implementing a planar
coordinate transformation on a 5D Ricci-flat metric solution, in the context of
a non-compact Kaluza-Klein theory of gravity. We found that the spectrum is
nearly scale invariant under certain conditions. One interesting aspect of this
model is that is possible to derive dynamical field equations for the tensor
metric fluctuations, valid not just at cosmological scales, but also at
astrophysical scales, from the same theoretical model. The astrophysical and
cosmological scales are determined by the gravity- antigravity radius, which is
a natural length scale of the model, that indicates when gravity becomes
repulsive in nature.
