Minimal Fine Tuning in Supersymmetric Higgs Inflation

We investigate characteristic features of realistic parameter choice for primordial inflation with supersymmetric Higgs inflaton as an example of particle physics inflation model. We discuss constraints from observational results and analyze the degree of fine tuning needed to induce slow-roll inflation for wide range of soft supersymmetry breaking scale. The observed amplitude of density fluctuations implies that the minimal fine tuning for the combined electroweak scale and inflaton flatness predicts the spectral index of 0.950--0.965, which includes the central value from observational data.