  We develop a minimal model to describe growing dense active matter such as
biological tissues, bacterial colonies and biofilms, that are driven by a
competition between particle division and steric repulsion. We provide a
detailed numerical analysis of collective and single particle dynamics. We show
that the microscopic dynamics can be understood as the superposition of an
affine radial component due to the global growth, and of a more complex
non-affine component which displays features typical of driven soft glassy
materials, such as aging, compressed exponential decay of time correlation
functions, and a crossover from superdiffusive behaviour at short scales to
subdiffusive behaviour at larger scales. This analogy emerges because particle
division at the microscale leads to a global expansion which then plays a role
analogous to shear flow in soft driven glasses. We conclude that growing dense
active matter and sheared dense suspensions can generically be described by the
same underlying physics.
