Non-minimally coupled hybrid inflation
  We discuss the hybrid inflation model where the inflaton field is
nonminimally coupled to gravity. In the Jordan frame, the potential contains
$\phi^4$ term as well as terms in the original hybrid inflation model. In our
model, inflation can be classified into the type (I) and the type (II). In the
type (I), inflation is terminated by the tachyonic instability of the waterfall
field, while in the type (II) by the violation of slow-roll conditions. In our
model, the reheating takes place only at the true minimum and even in the case
(II) finally the tachyonic instability occurs after the termination of
inflation. For a negative nonminimal coupling, inflation takes place in the
vacuum-dominated region, in the large field region, or near the local
minimum/maximum. Inflation in the vacuum dominated region becomes either the
type (I) or (II), resulting in blue or red spectrum of the curvature
perturbations, respectively. Inflation around the local maximum can be either
the type (I) or the type (II), which results in the red spectrum of the
curvature perturbations, while it around the local minimum must be the type
(I), which results in the blue spectrum. In the large field region, to
terminate inflation, potential in the Einstein frame must be positively tilted,
always resulting in the red spectrum. We then numerically solve the equations
of motion to investigate the whole dynamics of inflaton and confirm that the
spectrum of curvature perturbations changes from red to blue ones as scales
become smaller.
