  Within the ultrarelativistic quantum molecular dynamics (UrQMD) model, the
effect of initial density fluctuations on cumulants of the net-proton
multiplicity distribution in Au + Au Collisions at $\sqrt{s_{NN}}$ = 7.7 GeV
was investigated by varying the minimum distance $d_{\rm min}$ between two
nucleons in the initialization. It was found that the initial density
fluctuations increased with the decrease of $d_{\rm min}$ from 1.6 fm to 1.0
fm, and the influence of $d_{\rm min}$ on the magnitude of the net-proton
number fluctuation in a narrow pseudorapidity window ($\Delta \eta \leq$ 4) was
negligible even if it indeed affected the density evolution during the
collision. At a broad pseudorapidity window ($\Delta \eta \geq$ 4), the
cumulant ratios were enlarged when the initial density fluctuations were
increased with the smaller value of $d_{\rm min}$, and this enhancement was
comparable to that observed in the presence of the nuclear mean-field
potential. Moreover, the enhanced cumulants were more evident in collisions
with a larger impact parameter. The present work demonstrates that the
fingerprint of the initial density fluctuations on the cumulants in a broad
pseudorapidity window is clearly visible, while it is not obvious as the
pseudorapidity window becomes narrow.
