  We compute the entanglement and R\'enyi entropy growth after a global quench
in various dimensions in free scalar field theory. We study two types of
quenches: a boundary state quench and a global mass quench. Both of these
quenches are investigated for a strip geometry in 1, 2, and 3 spatial
dimensions, and for a spherical geometry in 2 and 3 spatial dimensions. We
compare the numerical results for massless free scalars in these geometries
with the predictions of the analytical quasiparticle model based on EPR pairs,
and find excellent agreement in the limit of large region sizes. At subleading
order in the region size, we observe an anomalous logarithmic growth of
entanglement coming from the zero mode of the scalar.
