Principal reconstructed modes of dark energy and gravity

Recently, in [1], we presented 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. The reconstruction was performed with and without a theory-informed prior, built on the general Horndeski class of scalar-tensor theories, that correlates the three functions. In this work, we perform a decomposition of the prior and posterior covariances of the three functions to determine the structure of the modes that are constrained by the data relative to the Horndeski prior. We find that the combination of all data can constrain 15 combined eigenmodes of the three functions with respect to the prior. We examine and interpret their features in view of the well-known tensions between datasets within the $\Lambda$CDM model. We also assess the bias introduced by the simplistic parameterizations commonly used in the literature for constraining deviations from GR on cosmological scales.