Supersymmetric hybrid inflation with non-minimal Kähler potential

Minimal supersymmetric hybrid inflation based on a minimal Kähler potential predicts a spectral index ns≳0.98. On the other hand, WMAP three year data prefers a central value ns≈0.95. We propose a class of supersymmetric hybrid inflation models based on the same minimal superpotential but with a non-minimal Kähler potential. Including radiative corrections using the one-loop effective potential, we show that the prediction for the spectral index is sensitive to the small non-minimal corrections, and can lead to a significantly red-tilted spectrum, in agreement with WMAP.