  Several earth-based gravitational-wave (GW) detectors are actively pursuing
the quest for placing observational constraints on models that predict the
behavior of a variety of astrophysical and cosmological sources. These sources
span a wide gamut, ranging from hydrodynamic instabilities in neutron stars
(such as r-modes) to particle production in the early universe. Signals from a
subset of these sources are expected to appear in these detectors as stochastic
GW backgrounds (SGWBs). The detection of these backgrounds will help us in
characterizing their sources. Accounting for such a background will also be
required by some detectors, such as the proposed space-based detector LISA, so
that they can detect other GW signals. Here, we formulate the problem of
constructing a bank of search templates that discretely span the parameter
space of a generic SGWB. We apply it to the specific case of a class of
cosmological SGWBs, known as the broken power-law models. We derive how the
template density varies in their three-dimensional parameter space and show
that for the LIGO 4km detector pair, with LIGO-I sensitivities, about a few
hundred templates will suffice to detect such a background while incurring a
loss in signal-to-noise ratio of no more than 3%.
