  The motion of the center of mass of a coalescing binary black hole (BBH) in a
gravitational potential imprints a line-of-sight acceleration (LOSA) onto the
emitted gravitational wave (GW) signal. The acceleration could be sufficiently
large in dense stellar environments, such as globular clusters (GCs), to be
detectable with next-generation space-based detectors. In this work, we use
outputs of the \textsc{cluster monte carlo (cmc)} simulations of dense star
clusters to forecast the distribution of detectable LOSAs in DECIGO and LISA
eras. We study the effect of cluster properties -- metallicity, virial and
galactocentric radii -- on the distribution of detectable accelerations,
account for cosmologically-motivated distributions of cluster formation times,
masses, and metallicities, and also incorporate the delay time between the
formation of BBHs and their merger in our analysis. We find that larger
metallicities provide a larger fraction of detectable accelerations by virtue
of a greater abundance of relatively lighter BBHs, which allow a higher number
of GW cycles in the detectable frequency band. Conversely, smaller
metallicities result in fewer detections, most of which come from relatively
more massive BBHs with fewer cycles but larger LOSAs. We similarly find
correlations between the virial radii of the clusters and the fractions of
detectable accelerations. Our work, therefore, provides an important science
case for space-based GW detectors in the context of probing GC properties via
the detection of LOSAs of merging BBHs.
