Running of Spectral Index for a Hybrid Inflationary Model

Abstract

A hybrid inflationary model with cubic potential where inflation ends in a different
way, due to very rapid rolling of an auxiliary scalar field ψ is discussed. The slowly rolling
inflation field φ does not account for the majority of the energy density in hybrid inflation.
Another field ψ takes this role, which is maintained in position by its interaction with φ until
φ falls below a critical value φ_c . When this occurs, ψ has been destabilized and inflation
comes to an end by rolling toward its true vacuum. In this model, the second derivative of
the inflaton potential, which represents its effective mass undergoes a sudden small change.
The spectral indices related to density perturbations n₁ and n₂ just before and soon after the
phase transition respectively are determined. It is found that the ensuing density perturbation
has a power spectrum that is nearly flat with a step in n_s