  We investigate the time-dependent R\'{e}nyi entanglement entropy after a
quantum quench starting from the Mott-insulating and charge-density-wave states
in a one-dimensional free boson system. The second R\'{e}nyi entanglement
entropy is found to be the negative of the logarithm of the permanent of a
matrix consisting of time-dependent single-particle correlation functions. From
this relation and a permanent inequality, we obtain rigorous conditions for
satisfying the volume-law entanglement growth. We also succeed in calculating
the time evolution of the R\'{e}nyi entanglement entropy in unprecedentedly
large systems by brute-force computations of the permanent. We discuss possible
applications of our findings to the real-time dynamics of noninteracting
bosonic systems.
