  We study the dynamics of a tracer particle (TP) on a comb lattice populated
by randomly moving hard-core particles in the dense limit. We first consider
the case where the TP is constrained to move on the backbone of the comb only,
and, in the limit of high density of particles, we present exact analytical
results for the cumulants of the TP position, showing a subdiffusive behavior
$\sim t^{3/4}$. At longer times, a second regime is observed, where standard
diffusion is recovered, with a surprising non analytical dependence of the
diffusion coefficient on the particle density. When the TP is allowed to visit
the teeth of the comb, based on a mean-field-like Continuous Time Random Walk
description, we unveil a rich and complex scenario, with several successive
subdiffusive regimes, resulting from the coupling between the inhomogeneous
comb geometry and particle interactions. Remarkably, the presence of hard-core
interactions speeds up the TP motion along the backbone of the structure in all
regimes.
