The gravitino abundance in supersymmetric ‘new’ inflation models

Using the equations recently presented by Kallosh et. al. (hep-th/9907124) and Giudice et. al. (hep-ph/9907510), we estimate the abundance of gravitinos created from the vacuum, in ‘new’ inflation models for which global supersymmetry is a good approximation. Gravitinos with helicity 1/2 are produced abundantly just after inflation, when their effective mass rises sharply, and even more abundantly later when it descends to the true mass. In a wide range of parameter space, they are more abundant than gravitinos created by thermal collisions, leading to significant constraints on the inflation model. Introduction Gravitinos are created in the early Universe with a cosmologically significant abundance. They are certainly created by thermal collisions after reheating [1], and some time ago [2] it was pointed out that they may also be created from the vacuum fluctuation during inflation. It was conjectured that the gravitino abundance from this mechanism would be no bigger than the abundance of spin 1/2 particles with gravitational-strength interactions (modulini), making it negligible compared [2] with the abundance from thermal collisions. Recently, the mode function equations determining the gravitino abundance have been worked out [3, 4], for the case of a single chiral superfield and the minimal kinetic term. On the basis of these equations, their authors have pointed out that gravitinos may be created much more abundantly than modulini. In this note, we see how this works out in a specific class [5] of models. The model In order to use the equations given in [3, 4], we must consider a model of inflation, based on a tree-level supergravity theory containing no physical fields except the gravitino, and a complex scalar field φ1 with the minimal kinetic term. (The