https://doi.org/10.1140/epjc/s10052-023-12230-2
Regular Article - Theoretical Physics
Minimal length scale correction in the noise of gravitons
Department of Astrophysics and High Energy Physics, S. N. Bose National Centre for Basic Sciences, JD Block, Sector-III, 700 106, Salt Lake City, Kolkata, India
Received:
20
June
2023
Accepted:
5
November
2023
Published online:
16
November
2023
In this paper we have considered a quantized and linearly polarized gravitational wave interacting with a gravitational wave detector (interferometer detector) in the generalized uncertainty principle (GUP) framework. Following the analysis in Phys. Rev. Lett. 127:081602 (2021), we consider a quantized gravitational wave interacting with a gravitational wave detector (LIGO/VIRGO etc.) using a path integral approach. Although the incoming gravitational wave was quantized, no Planck-scale quantization effects were considered for the detector in earlier literatures. In our work, we consider a modified Heisenberg uncertainty relation with a quadratic order correction in the momentum variable between the two phase space coordinates of the detector. Using a path integral approach, we have obtained a stochastic equation involving the separation between two point-like objects. It is observed that random fluctuations (noises) and the correction terms due to the generalized uncertainty relation plays a crucial role in dictating such trajectories. Finally, we observe that the solution to the stochastic equation leads to time dependent standard deviation due to the GUP insertion, and for a primordial gravitational wave (where the initial state is a squeezed state) both the noise effect and the GUP effects exponentially enhance which may be possible to detect in future generation of gravitational wave detectors. We have also given a plot of the dimensionless standard deviation with time depicting that the GUP effect will carry a distinct signature which may be detectable in the future space based gravitational wave observatories.
© The Author(s) 2023
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