Parameter splitting in dark energy: is dark energy the same in the background and in the cosmic structures?

We perform an empirical consistency test of General Relativity/dark energy by disentangling expansion history and growth of structure constraints. We replace each late-universe parameter that describes the behavior of dark energy with two meta-parameters: one describing geometrical information in cosmological probes, and the other controlling the growth of structure. If the underlying model (a standard wCDM cosmology with General Relativity) is correct, that is under the null hypothesis, the two meta-parameters coincide. If they do not, it could indicate a failure of the model or systematics in the data. We present a global analysis using state-of-the-art cosmological data sets which points in the direction that cosmic structures prefer a weaker growth than that inferred by background probes. This result could signify inconsistencies of the model, the necessity of extensions to it or the presence of systematic errors in the data. We examine all these possibilities. The fact that the result is mostly driven by a specific sub-set of galaxy clusters abundance data, points to the need of a better understanding of this probe.