Generalized uncertainty principle in bar detectors of gravitational waves

TL;DR

This paper explores how the generalized uncertainty principle affects the response of gravitational wave bar detectors, calculating resonant frequencies and transition rates to identify potential quantum gravity effects.

Contribution

It introduces a framework to analyze the impact of the generalized uncertainty principle on gravitational wave detectors' vibrations and responses.

Findings

Calculated resonant frequencies under GUP framework

Estimated transition rates induced by gravitational waves

Proposed experimental bounds on GUP parameters

Abstract

At present the gravitational waves 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 it becomes quite obvious to search for the generalized uncertainty principle by observing the response of the vibrations of phonon modes in such resonant detectors in the near future. Therefore, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors in the generalized uncertainty principle framework. This presentation is based on the work published in \cite{sb2}.