Model-independent reconstruction of the interacting dark energy kernel: Binned and Gaussian process

The cosmological dark sector remains an enigma, offering numerous possibilities for exploration. One particularly intriguing option is the (non-minimal) interaction scenario between dark matter and dark energy. In this paper, to investigate this scenario, we have implemented Binned and Gaussian model-independent reconstructions for the interaction kernel alongside the equation of state; while using data from BAOs, Pantheon+ and Cosmic Chronometers. In addition to the reconstruction process, we conducted a model selection to analyze how our methodology performed against the standard ΛCDM model. The results revealed a slight indication, of at least 1σ confidence level, for some oscillatory dynamics in the interaction kernel and, as a by-product, also in the DE and DM. A consequence of this outcome is the possibility of a sign change in the direction of the energy transfer between DE and DM and a possible transition from a negative DE energy density in early-times to a positive one at late-times. While our reconstructions provided a better fit to the data compared to the standard model, the Bayesian Evidence showed an intrinsic penalization due to the extra degrees of freedom. Nevertheless these reconstructions could be used as a basis for other physical models with lower complexity but similar behavior.