  Epithelial cell tissues have a slow relaxation dynamics resembling that of
supercooled liquids. Yet, they also have distinguishing features. These include
an extended short-time sub-diffusive transient, as observed in some experiments
and recent studies of model systems, and a sub-Arrhenius dependence of the
relaxation time on temperature, as reported in numerical studies. Here we
demonstrate that the anomalous glassy dynamics of epithelial tissues originates
from the emergence of a fractal-like energy landscape, particles becoming
virtually free to diffuse in specific phase space directions up to a small
distance. Furthermore, we clarify that the stiffness of the cells tunes this
anomalous behaviour, tissues of stiff cells having conventional glassy
relaxation dynamics.
