Generalized uncertainty principle in resonant detectors of gravitational waves

TL;DR

This paper explores how the generalized uncertainty principle influences the response of gravitational wave resonant detectors, calculating frequency shifts and transition rates, and providing bounds on the GUP parameter based on detector sensitivities.

Contribution

It introduces a framework to analyze GUP effects on resonant gravitational wave detectors, including calculations of frequency shifts and bounds on GUP parameters.

Findings

GUP affects both time-independent and dependent parts of the Hamiltonian.

Resonant frequencies and transition rates are modified by GUP effects.

Upper bounds on the GUP parameter are estimated from detector sensitivities.

Abstract

With the direct detection of gravitational waves 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 ($\delta L$), $\mathcal{O} \approx 10^{-17}-10^{-21}$ meter. Recently a more stringent upperbound on the dimensionless parameter $\beta_0$, bearing the effect of generalized uncertainty principle has been given which corresponds to the intermediate length scale $l_{im}= \sqrt{\beta_0} l_{pl} \sim 10^{-23} m$. Hence the flavour of the generalized uncertainty principle 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 gravitational waves on these detectors in the generalized uncertainty principle framework. It is observed that the effects of the generalized uncertainty principle 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.