The dynamics of a reduced cosmic density matrix for minisuperspace is derived by projecting out inhomogeneous modes. This projection procedure roughly represents the intrinsic loss of information beyond the horizon of the local observer. Even if the wave function of the whole Universe exists, it will be unobservable and therefore should be projected onto actually accessible dynamics. We use a simple model of the homogeneous Robertson-Walker universe with an inhomogeneous scalar field. The path-integral expression for the density matrix is derived and evaluated by the steepest-descent method. We show that the cosmic expansion reduces the quantum coherence of the scale factor and simultaneously that of the canonically conjugate momentum.