Non-Gaussianity and finite length inflation

Abstract

In the present paper, certain inflation models are shown to have large non-Gaussianity in special cases. Namely, finite length inflation models with an effective higher derivative interaction, in which slow-roll inflation is adopted as inflation and a scalar-matter-dominated period or power inflation is adopted as pre-inflation, are considered. Using Holman and Tolley's formula of the nonlinearity parameter $f^\textrm{\tiny flattened}_\textrm{\tiny NL}$, we calculate the value of $f^\textrm{\tiny flattened}_\textrm{\tiny NL}$. A large value of $f^\textrm{\tiny flattened}_\textrm{\tiny NL}(f^\textrm{\tiny flattened}_\textrm{\tiny NL} > 100)$ can be obtained for all of the models considered herein when the length of inflation is 60-63 $e$-folds and $f_\textrm{\tiny NL}$ has strong dependence on the length of inflation. Interestingly, this length is similar to that for the case in which the suppression of the CMB angular power spectrum of $l=2$ was derived using the inflation models described in our previous papers.