  The discovery of superconductivity in infinite-layer nickelates is presently
an important topic in condensed-matter physics, and potential similarities to
and differences from cuprates are under intense debate. We determine general
features of the charge excitation spectrum in nickelates from two opposite
viewpoints: (i) Nickelates are regarded as strongly correlated electron systems
like cuprate superconductors and thus can be described by the $t$-$J$ model,
and (ii) electron correlation effects are not as strong as in cuprates, and
thus, random-phase approximation (RPA) calculations may capture the essential
physics. We find that in both cases, plasmon excitations are realized around
the momentum transfer $\vq=(0,0,q_z)$, although they tend to be damped more
strongly in the RPA. In particular, this damping is enhanced by the relatively
large interlayer hopping expected in nickelates. Besides reproducing the
optical plasmon at $\vq=(0,0,0)$ observed in Nd$_{0.8}$Sr$_{0.2}$NiO$_2$, we
obtain low-energy plasmons with gaps of $\sim 360$ and $\sim 560$ meV at
$\vq=(0,0,q_z)$ for finite $q_z$ in cases (i) and (ii), respectively. The
present work offers a possible theoretical hint to answer whether nickelates
are cupratelike or not and contributes to the general understanding of the
charge dynamics in nickelates.
