We present the first combined non-parametric reconstruction of the three time-dependent functions that capture departures from the standard cosmological model, $Lambda$CDM, in the expansion history and gravitational effects on matter and light from the currently available combination of the background and large scale structure data. We perform the reconstruction with and without a theory-informed prior, built on the general Horndeski class of scalar-tensor theories, that correlates the three functions. We find that the combination of all data can constrain 15 combined eigenmodes of the three functions with respect to the prior, allowing for an informative reconstruction of the cosmological model featuring non-trivial time-dependences. We interpret the latter in the context of the well-known tensions between some of the datasets within $Lambda$CDM, along with discussing implications of our reconstruction for modified gravity theories.
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