Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework

TL;DR

This paper investigates how generalized uncertainty principles affect gravitational wave detectors, revealing modifications in energy states and transition rates, and establishing bounds on GUP parameters based on these effects.

Contribution

It introduces a novel analysis of resonant gravitational wave detectors within linear and quadratic GUP frameworks, highlighting the impact on energy eigenstates and transition probabilities.

Findings

GUP modifies the resonant frequencies and energy eigenvalues.

Linear GUP introduces non-zero transition probabilities between energy levels.

Bounds on GUP parameters are derived from transition rate analysis.

Abstract

In this work, we consider a resonant bar detector of gravitational wave in the generalized uncertainty principle (GUP) framework with linear and quadratic momentum uncertainties. The phonon modes in these detectors vibrate due to the interaction with the incoming gravitational wave. In this uncertainty principle framework, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors. We observe that the energy eigenstates and the eigenvalues get modified by the GUP parameters. We also observe non-vanishing transition probabilities between two adjacent energy levels due to the existence of the linear order momentum correction in the generalized uncertainty relation which was not present in the quadratic GUP analysis [http://dx.doi.org/10.1088/1361-6382/abac45, Class. Quantum Grav. 37 (2020) 195006]. We finally obtain bounds on the dimensionless GUP parameters using the form of the transition rates obtained during this analysis.