In general relativity, a gravitational wave has two polarization modes
(tensor mode), but it could have additional polarizations (scalar and vector
modes) in the early stage of the universe, where the general relativity may not
strictly hold and/or the effect of higher-dimensional gravity may become
significant. In this paper, we discuss how to detect extra-polarization modes
of stochastic gravitational wave background (GWB), and study the separability
of each polarization using future space-based detectors such as BBO and DECIGO.
We specifically consider two plausible setups of the spacecraft constellations
consisting of two and four clusters, and estimate the sensitivity to each
polarization mode of GWBs. We find that a separate detection of each
polarization mode is rather sensitive to the geometric configuration and
distance between clusters and that the clusters should be, in general,
separated by an appropriate distance. This seriously degrades the signal
sensitivity, however, for suitable conditions, space-based detector can
separately detect scalar, vector and tensor modes of GWBs with energy density
as low as ~10^-15.Comment: 16 pages, 11 figure