Search templates for stochastic gravitational-wave backgrounds

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 these backgrounds 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 4 km detector pair, with LIGO-I sensitivities, 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%.