Probing nontensorial polarizations of stochastic gravitational-wave backgrounds with ground-based laser interferometers

In a general metric theory of gravitation in four dimensions, six polarizations of a gravitational wave are allowed: two scalar and two vector modes, in addition to two tensor modes in general relativity. Such additional polarization modes appear due to additional degrees of freedom in modified theories of gravitation or theories with extra dimensions. Thus, observations of gravitational waves can be utilized to constrain the extended models of gravitation. In this paper, we investigate detectability of additional polarization modes of gravitational waves, particularly focusing on a stochastic gravitational-wave background, with laser-interferometric detectors on the Earth. We found that more than three detectors can separate the mixture of polarization modes in detector outputs, and that they have almost the same sensitivity to each polarization mode of stochastic gravitational-wave background.