Investigating bounds on the extended uncertainty principle metric through astrophysical tests

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.