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.
