Model independent inference of the expansion history and implications for the growth of structure

We model the expansion history of the Universe as a Gaussian Process and find constraints on the dark energy density and its low-redshift evolution using distances inferred from the Luminous Red Galaxy (LRG) and Lyman-alpha (Ly$\alpha$) datasets of the Baryon Oscillation Spectroscopic Survey, supernova data from the Joint Light-curve Analysis (JLA) sample, Cosmic Microwave Background (CMB) data from the Planck satellite, and local measurement of the Hubble parameter from the Hubble Space Telescope ($\mathsf{H}0$). Our analysis shows that the CMB, LRG, Ly$\alpha$, and JLA data are consistent with each other and with a $\mathrm{\Lambda }$CDM cosmology, but the $\mathsf{H}0$ data is inconsistent at moderate significance. Including the presence of dark radiation does not alleviate the $\mathsf{H}0$ tension in our analysis. While some of these results have been noted previously, the strength here lies in that we do not assume a particular cosmological model. We calculate the growth of the gravitational potential in General Relativity corresponding to these general expansion histories and show that they are well-approximated by $\Omega_{\rm m}^{0.55}$ given the current precision. We assess the prospects for upcoming surveys to measure deviations from $\mathrm{\Lambda }$CDM using this model-independent approach.