Investigating bounds on the extended uncertainty principle metric through astrophysical tests

TL;DR

This study tests the extended uncertainty principle (EUP) metric using astrophysical observations, deriving bounds on its fundamental length scale from phenomena like gravitational redshift and orbital precession.

Contribution

It provides the first comprehensive astrophysical constraints on the EUP metric's fundamental length scale through multiple gravitational tests.

Findings

Lower bound on EUP length scale from gravitational redshift (~0.09 m)

Upper bound from S2 star orbit precession (~4×10^{10} m)

Constraints help refine quantum gravity models at large scales.

Abstract

In this paper, we consider the gravitational tests for the extended uncertainty principle (EUP) metric, which is a large-scale quantum correction to Schwarzschild metric. We calculate gravitational redshift, geodetic precession, Shapiro time delay, precession of Mercury and S2 star's orbits. Using the results of experiments and observations, we obtain the lower bounds for the EUP fundamental length scale $L_{*}$. We obtain the smallest bound $L_{*} \sim9\times 10^{-2}$m for gravitational redshift, and the largest bound $L_{*} \sim4\times 10^{10}$m for the precession of S2's orbit.