  We study quantum tunneling for the de Sitter radiation in the planar
coordinates and global coordinates, which are nonstationary coordinates and
describe the expanding geometry. Using the phase-integral approximation for the
Hamilton-Jacobi action in the complex plane of time, we obtain the
particle-production rate in both coordinates and derive the additional
sinusoidal factor depending on the dimensionality of spacetime and the quantum
number for spherical harmonics in the global coordinates. This approach
resolves the factor of two problem in the tunneling method.
