A universal secondary relaxation process, known as the Johari-Goldstein (JG) $beta$-relaxation process, appears in glass formers. It involves all parts of the molecule and is particularly important in glassy systems because of its very close relationship with the $alpha$-relaxation process. However, the absence of a J-G $beta$-relaxation mode in colloidal glasses raises questions regarding its universality. In the present work, we study the microscopic relaxation processes in Laponite suspensions, a model soft glassy material, by dynamic light scattering (DLS) experiments. $alpha$ and $beta$-relaxation timescales are estimated from the autocorrelation functions obtained by DLS measurements for Laponite suspensions with different concentrations, salt concentrations and temperatures. Our experimental results suggest that the $beta$-relaxation process in Laponite suspensions involves all parts of the constituent Laponite particle. The ergodicity breaking time is also seen to be correlated with the characteristic time of the $beta$-relaxation process for all Laponite concentrations, salt concentrations and temperatures. The width of the primary relaxation process is observed to be correlated with the secondary relaxation time. The secondary relaxation time is also very sensitive to the concentration of Laponite. We measure primitive relaxation timescales from the $alpha$-relaxation time and the stretching exponent ($beta$) by applying the coupling model for highly correlated systems. The order of magnitude of the primitive relaxation time is very close to the secondary relaxation time. These observations indicate the presence of a J-G $beta$-relaxation mode for soft colloidal suspensions of Laponite.
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