Footprint of spatial noncommutativity in resonant detectors of gravitational wave

The present day gravitational wave (GW) detectors strive to detect the length variation , which, owing to the smallness of the metric perturbation h, is an extremely small length -10−21 m. The recently proposed noncommutative structure of space has a characteristic length-scale which has an estimated upper-bound in similar length-scale range. We therefore propose that GW data can be used as an effective probe of noncommutative structure of space. In this paper we demonstrate how spatial noncommutativity modifies the responding frequency of the resonant detectors of GW and also the corresponding probabilities of GW induced transitions that the phonon modes of such resonant detectors undergo. We present the complete perturbative calculation involving both time-independent and time-dependent perturbations in the Hamiltonian.