  Dynamical heterogeneities -- strong fluctuations near the glass transition --
are believed to be crucial to explain much of the glass transition
phenomenology. One possible hypothesis for their origin is that they emerge
from soft (Goldstone) modes associated with a broken continuous symmetry under
time reparametrizations. To test this hypothesis, we use numerical simulation
data from four glass-forming models to construct coarse grained observables
that probe the dynamical heterogeneity, and decompose the fluctuations of these
observables into two transverse components associated with the postulated
time-fluctuation soft modes and a longitudinal component unrelated to them. We
find that as temperature is lowered and timescales are increased, the time
reparametrization fluctuations become increasingly dominant, and that their
correlation volumes grow together with the correlation volumes of the dynamical
heterogeneities, while the correlation volumes for longitudinal fluctuations
remain small.
