Inflationary solutions in the nonminimally coupled scalar field theory

We study analytically and numerically the inflationary solutions for various type scalar potentials in the nonminimally coupled scalar field theory. The Hamilton-Jacobi equation is used to deal with nonlinear evolutions of inhomogeneous spacetimes and the long-wavelength approximation is employed to find the homogeneous solutions during an inflation period. The constraints that lead to a sufficient number of e-folds, a necessary condition for inflation, are found for the nonminimal coupling constant and initial conditions of the scalar field for inflation potentials. In particular, we numerically find an inflationary solution in the new inflation model of a nonminimal scalar field.