Kähler potentials for the MSSM inflation and the spectral index

Recently it has been argued that some of the fine-tuning problems of the MSSM inflation associated with the existence of a saddle point along a flat direction may be solved naturally in a class of supergravity models. Here we extend the analysis and show that the constraints on the Kähler potentials in these models are considerably relaxed when the location of the saddle point is treated as a free variable. We also examine the effect of supergravity corrections on inflationary predictions and find that they can slightly alter the value of the spectral index. As an example, for flat direction field values |φ̄0| = 1×10MP we find n ∼ 0.92 ... 0.94 while the prediction of the MSSM inflation without any corrections is n ∼ 0.92.