Stochastic gravitational wave backgrounds, predicted in many models of the early universe and also generated by various astrophysical processes, are a powerful probe of the Universe. The spectral shape is key information to distinguish the origin of the background since different production mechanisms predict different shapes of the spectrum. In this paper, we investigate how precisely future gravitational wave detectors can determine the spectral shape using single and broken power-law templates. We consider the detector network of Advanced-LIGO, Advanced-Virgo and KAGRA and the space-based gravitational-wave detector DECIGO, and estimate the parameter space which could be explored by these detectors. We find that, when the spectrum changes its slope in the frequency range of the sensitivity, the broken power-law templates dramatically improve the $chi^2$ fit compared with the single power-law templates and help to measure the shape with a good precision.
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