We combine cosmic chronometer and growth of structure data to derive the redshift evolution of the dark energy equation of state w, using a novel agnostic approach. The background and perturbation equations lead to two expressions for w, one purely background-based and the other relying also on the growth rate of large-scale structure. We compare the features and performance of the growth-based w to the background w, using Gaussian Processes for the reconstructions. We find that current data is not precise enough for robust reconstruction of the two forms of w. By using mock data expected from next-generation surveys, we show that the reconstructions will be robust enough and that the growth-based w will out-perform the background w. Furthermore, any disagreement between the two forms of w will provide a new test for deviations from the standard model of cosmology.
Reference:
Measuring dark energy with expansion and growth, Louis Perenon, Matteo Martinelli, Roy Maartens, Stefano Camera, Chris Clarkson, arXiv:2206.12375