WHAT ARE THE Omh2 (z1, z2) AND Om (z1, z2) DIAGNOSTICS TELLING US IN LIGHT OF H(z) DATA?

ABSTRACT The two-point diagnostics Om ( z i , z j ) and Omh 2 ( z i , z j ) have been introduced as an interesting tool for testing the validity of the Λ cold dark matter (ΛCDM) model. Recently, Sahni et al. combined two independent measurements of H ( z ) from baryon acoustic oscillation (BAO) data with the value of the Hubble constant H 0 , and used the second of these diagnostics to test the ΛCDM (a constant equation-of-state parameter for dark energy) model. Their result indicated a considerable tension between observations and predictions of the ΛCDM model. Since reliable data concerning the expansion rates of the universe at different redshifts H ( z ) are crucial for the successful application of this method, we investigate both two-point diagnostics on the most comprehensive set of N = 36 measurements of H ( z ) from BAOs and the differential ages (DAs) of passively evolving galaxies. We discuss the uncertainties of the two-point diagnostics and find that they are strongly non-Gaussian and follow the patterns deeply rooted in their very construction. Therefore we propose that non-parametric median statistics is the most appropriate way of treating this problem. Our results support the claims that ΛCDM is in tension with H ( z ) data according to the two-point diagnostics developed by Shafieloo, Sahni, and Starobinsky. However, other alternatives to the ΛCDM model, such as the wCDM or Chevalier–Polarski–Linder models, perform even worse. We also note that there are serious systematic differences between the BAO and DA methods that ought to be better understood before H ( z ) measurements can compete with other probes methods.