  We present a two stage hybrid inflationary scenario in non-minimal
supergravity which can predict values of the tensor-to-scalar ratio of the
order of few times 0.01. For the parameters considered, the underlying
supersymmetric particle physics model possesses two inflationary paths, the
trivial and the semi-shifted one. The trivial path is stabilized by
supergravity corrections and supports a first stage of inflation with a limited
number of e-foldings. The tensor-to-scalar ratio can become appreciable while
the value of the scalar spectral index remains acceptable as a result of the
competition between the relatively mild supergravity corrections and the strong
radiative corrections to the inflationary potential. The additional number of
e-foldings required for solving the puzzles of hot big bang cosmology are
generated by a second stage of inflation taking place along the semi-shifted
path. This is possible only because the semi-shifted path is almost
perpendicular to the trivial one and, thus, not affected by the strong
radiative corrections along the trivial path and also because the supergravity
effects remain mild. The requirement that the running of the scalar spectral
index remains acceptable limits the possible values of the tensor-to-scalar
ratio not to exceed about 0.05. Our model predicts the formation of an unstable
string-monopole network, which may lead to detectable gravity wave signatures
in future space-based laser interferometer observations.
