Klein-Gordon equation in Riemannian space

A solution that depends on $a(t)$ is obtained for the Klein–Gordon equation in the metric of a closed Fridman model. The metric's being non-Euclidean and time-dependent leads to the wave function's being damped in the f i r s t order and the frequency's being reduced in the second order of an expansion in the small parameter $H/\omega_0\sim10^{-40}$.