Time-dependent couplings in the dark sector: from background evolution to non-linear structure formation

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 behaviours between the standard Lambda CDM 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 non-linear 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 Lambda CDM, contrarily to what happens for constant coupling models where concentrations can only decrease. However, for some specific choice of the interaction function, the reduction in halo concentrations can be larger than in constant coupling scenarios. We also find that different types of coupling evolution determine specific features in the growth of large-scale structures, like peculiar distortions of the matter power spectrum shape or different time-evolutions of the halo mass function. Furthermore, also for time-dependent couplings, baryons and CDM develop a bias already on large scales, which is progressively enhanced for smaller and smaller scales, and the effect can be significantly larger compared to constant coupling scenarios. The same happens to the baryon fraction of haloes, which can be more significantly reduced below its universal value in variable coupling models with respect to constant coupling cosmologies. 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 Lambda CDM model on small scales than the constant coupling scenario.