  A double hybrid inflationary scenario in non-minimal supergravity which can
predict values of the tensor-to-scalar ratio up to about 0.05 is presented.
Larger values of this ratio would require unacceptably large running of the
scalar spectral index. The underlying supersymmetric particle physics model
possesses, for the chosen values of the parameters, practically two
inflationary paths, the trivial and the semi-shifted one. The trivial path is
stabilized by supergravity and supports a first stage of inflation with a
limited number of e-foldings. The tensor-to-scalar ratio can become appreciable
with the scalar spectral index remaining acceptable, as a result of the
competition between the relatively mild supergravity 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 along the semi-shifted path. This is possible only
because the semi-shifted path is almost orthogonal to the trivial one and,
thus, not affected by the strong radiative corrections on the trivial path and
also because the supergravity effects remain mild. The model predicts the
formation of an unstable network of open cosmic strings connecting monopoles to
antimonopoles. This network decays to gravity waves well before recombination
leading to possibly detectable signatures in future space-based laser
interferometer gravitational-wave detectors.
