  We investigate how inhomogeneous quintessence models may have a specific
signature even in the linear regime of large scale structure formation. The
dynamics of the collapse of a dark matter halo is governed by the value or the
dynamical evolution of the dark energy equation of state, the energy density's
initial conditions and its homogeneity nature in the highly non-linear regime.
These have a direct impact on the redshift of collapse, altering in consequence
the linearly extrapolated density threshold above which structures will end up
collapsing. We compute this quantity for minimally coupled and coupled
quintessence models, examining two extreme scenarios: first, when the
quintessence field does not exhibit fluctuations on cluster scales and below -
homogeneous dark energy; and second, when the field inside the overdensity
collapses along with the dark matter - inhomogeneous dark energy. One shows
that inhomogeneous dark energy models present distinct features which may be
used to confront them with observational data, for instance galaxy number
counting. Fitting formulae for the linearly extrapolated density threshold
above which structures will end up collapsing are provided for models of dark
energy with constant equation of state.

Astrophysics