M\"ossbauer spectroscopy study of magnetic fluctuations in superconducting RbGd$_2$Fe$_4$As$_4$O$_2$

$^{57}$Fe M\"ossbauer spectra were measured at different temperatures between 5.9 K and 300 K on the recently discovered self-doped superconducting RbGd$_2$Fe$_4$As$_4$O$_2$ with T$_c$ as high as 35 K. Singlet pattern was observed down to the lowest temperature measured in this work, indicating the absence of static magnetic order on the Fe site. The intermediate isomer shift in comparison with that of the samples RbFe$_2$As$_2$ and GdFeAsO confirms the self doping induced local electronic structure change. Surprisingly, we observe two magnetic fluctuation induced spectral broadenings below $\sim$15 K and $\sim$100 K which are believed to be originated from the transferred magnetic fluctuations of the Gd$^{3+}$ moments and that of the magnetic fluctuations of the Fe atoms, respectively.