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Gravitino Overproduction in Inflaton Decay

Most of the inflation models end up with non-vanishing vacuum expectation values of the inflaton fields ϕin the true vacuum, which induce, in general, nonvanishing auxiliary field G_ϕfor the inflaton potential in supergravity. We show that the presence of nonzero G_ϕgives rise to inflaton decay into a pair of the gravitinos and are thereby severely constrained by cosmology especially if the gravitino is unstable and its mass is in a range of O(100) GeV \sim O(10) TeV. For several inflation models, we explicitly calculate the values of G_ϕand find that most of them are excluded or on the verge of being excluded for the gravitino mass in that range. We conclude that an inflation model with vanishing G_ϕ, typically realized in a chaotic inflation, is favored in a sense that it naturally avoids the potential gravitino overproduction problem.