Imprints of cosmological tensions in reconstructed gravity

There has been a significant interest in modifications of the standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmological model prompted by tensions between certain datasets, most notably the Hubble tension. The late-time modifications of the $\Lambda$CDM model can be parametrized by three time-dependent functions describing the expansion history of the Universe and gravitational effects on light and matter in the Large Scale Structure. We perform the first joint Bayesian reconstruction of these three functions from a combination of recent cosmological observations, utilizing a theory-informed prior built on the general Horndeski class of scalar-tensor theories. This reconstruction is interpreted in light of the well-known $H_0$, the $S_8$ and the $A_L$ tensions. We identify the phenomenological features that alternative theories would need to have in order to ease some of the tensions, and deduce important constraints on broad classes of modified gravity models. Among other things, our findings suggest that late-time dynamical dark energy and modifications of gravity are not likely to offer a solution to the Hubble tension, or simultaneously solve the $A_L$ and $S_8$ tensions.