Cosmological constraints from a joint analysis of cosmic growth and expansion

Combining measurements on the expansion history of the Universe and on the growth rate of cosmic structures is key to discriminate between alternative cosmological frameworks and to test gravity. Recently, Linder (2017) proposed a new diagram to investigate the joint evolutionary track of these two quantities. In this letter, we collect the most recent cosmic growth and expansion rate datasets to provide the state-of-the-art observational constraints on this diagram. By performing a joint statistical analysis of both probes, we test the standard $\Lambda$CDM model, confirming a mild tension between cosmic microwave background predictions from Planck mission and cosmic growth measurements at low redshift ($z<2$). Then we test alternative models allowing the variation of one single cosmological parameter at a time. In particular, we find a larger growth index than the one predicted by general relativity $\gamma=0.65^{+0.05}_{-0.04}$). However, also a standard model with total neutrino mass of $0.26\pm0.10$ eV provides a similarly accurate description of the current data. By simulating an additional dataset consistent with next-generation dark-energy mission forecasts, we show that growth rate constraints at $z>1$ will be crucial to discriminate between alternative models.