Generalized uncertainty principle in resonant detectors of gravitational waves

Abstract

Abstract With the direct detection of gravitational waves (GWs) by advanced LIGO detector, a new ‘window’ to quantum gravity phenomenology has been opened. At present, these detectors achieve the sensitivity to detect the length variation (δL), O ≈ 1 0 − 17 − 1 0 − 21 metre. Recently a more stringent upperbound on the dimensionless parameter β 0, bearing the effect of generalized uncertainty principle (GUP) has been given which corresponds to the intermediate length scale l i m = β 0 l p l ∼ 1 0 − 23 m . Hence the flavour of the GUP can be realised by observing the response of the vibrations of phonon modes in such resonant detectors in the near future. In this paper, therefore, we calculate the resonant frequencies and transition rates induced by the incoming GWs on these detectors in the GUP framework. It is observed that the effects of the GUP bears its signature in both the time independent and dependent part of the gravitational wave-harmonic oscillator Hamiltonian. We also make an upper bound estimate of the GUP parameter.