Linear Term Inflation from Running Kinetic Term in Supergravity

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We propose a new class of inflation models in which the coefficient of the inflaton kinetic term rapidly changes with energy scale. This naturally occurs especially if the inflaton moves over a long distance during inflation as in the case of large-scale inflation. The peculiar behavior of the kinetic term opens up a new way to construct an inflation model. As a concrete example we construct a linear inflation model in supergravity. It is straightforward to build a chaotic inflation model with a fractional power along the same line. Interestingly, the potential takes a different form after inflation because of the running kinetic term. The inflation has been strongly motivated by the observation, 1) while it is a non-trivial task to construct a successful inflation model. A successful inflaton model must explain several features of the density perturbation, but properties of the inflaton are not well understood. It is often assumed that, in the slow-roll inflation paradigm, the inflaton is a weakly coupled field, and therefore the kinetic term is simply set to be the canonical form during inflation. This seems justified because the typical energy scale of inflation is given by the Hubble parameter, which remains almost constant during inflation. However, there is another important energy scale, namely, the inflaton field. Even in the slow-roll inflation, the motion of the inflaton is not negligible and it may travel a long distance during the whole period of inflation. In particular, in the case of large-scale inflation such as a chaotic inflation model, 2) the inflaton typically moves over a Planck scale or even larger within the last 60 e-foldings. 3) Then, it seems quite generic that the precise form of the kinetic term changes during the course of inflation. In some cases, the change could be so rapid, that it significantly affects the inflaton dynamics. In this letter, we construct a model in which the coefficient of the kinetic term grows rapidly with the inflaton field value, but in a controlled way. By doing so, we construct a linear term inflation model in the supergravity framework (see Ref. 4) for the quadratic model). The realization of the linear term inflation model in the string theory was given in Ref. 5). We also show that a chaotic inflation model with a fractional power can be straightforwardly constructed along the same line. Before going to a realistic inflation model, let us give our basic idea. Suppose that the inflaton field φ has the following kinetic term, LK = 1 f (φ) ∂ μ φ∂μφ,