Supersymmetric hybrid inflation with minimal and non-minimal Kähler potential

Minimal supersymmetric hybrid inflation based on a minimal Kahler potential predicts a spectral index n s ≥ 0.98. On the other hand, WMAP three-year data prefer a central value n s ≈ 0.95. We propose a class of supersymmetric hybrid inflation models based on the same minimal superpotential but with a non-minimal Kahler 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.