  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.
