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.
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