Probing the massive scalar mode in the levitated sensor detector of gravitational wave

Abstract

Owing to the mass scale associated with it the scalar longitudinal polarization mode of gravitational wave predicted in various modified theories of gravity should propagate at a subluminal speed and thus arrive with a time delay (for burst signals) or a phase difference (for persistent signals) at the detector site compared to the massless tensor polarization modes which move at the speed of light and are present in both standard general relativity and modified theories. The longitudinal massive scalar mode interacts non-trivially with detectors along the signal propagation direction in contrast to massless the tensor modes which interact only in the transverse plane. Identifying the signature of these distinctive features in a gravitational wave signal can provide observational evidence in favour of modified theories of gravity over general relativity. In this work we argue that owing to its compact design and tunability of operational frequency the recently proposed levitated sensor detectors \cite{Aggarwal} that works on the principle of gravitational wave induced resonant oscillation of a optically trapped \cite{Ashkin_1970} dielectric nanosphere sensor \cite{Geraci} can be useful in this regard. We demonstrate that the dynamics of the levitated sensor mass obeys a geodesic deviation equation in the proper detector frame and construct a quantum mechanical description of this system in modified gravity framework to compute the probabilities of resonant transitions in response to incoming gravitational wave signals of both periodic and aperiodic kind.

14 pages LaTex, no figure, revision