We present a complete numerical study of cosmological models with a time
dependent coupling between the dark energy component driving the present
accelerated expansion of the Universe and the Cold Dark Matter (CDM) fluid.
Depending on the functional form of the coupling strength, these models show a
range of possible intermediate behaviors between the standard LCDM background
evolution and the widely studied case of interacting dark energy models with a
constant coupling. These different background evolutions play a crucial role in
the growth of cosmic structures, and determine strikingly different effects of
the coupling on the internal dynamics of nonlinear objects. By means of a
suitable modification of the cosmological N-body code GADGET-2 we have
performed a series of high-resolution N-body simulations of structure formation
in the context of interacting dark energy models with variable couplings.
Depending on the type of background evolution, the halo density profiles are
found to be either less or more concentrated with respect to LCDM, contrarily
to what happens for constant coupling models where concentrations can only
decrease. However, for some specific choice of the interaction function the
reduction of halo concentrations can be larger than in constant coupling
scenarios. In general, we find that time dependent interactions between dark
energy and CDM can in some cases determine stronger effects on structure
formation as compared to the constant coupling case, with a significantly
weaker impact on the background evolution of the Universe, and might therefore
provide a more viable possibility to alleviate the tensions between
observations and the LCDM model on small scales than the constant coupling
scenario. [Abridged]Comment: 27 pages, 17 figures, 3 tables. Minor revisions. MNRAS accepte
